Exam 3 Ch 21 & 22

The magnetic flux through a coil of wire changes from 7.0 T m2 to 1.0 T m2 in 2.0 seconds. What is the magnitude of the average voltage induced in the coil during this change?

According to Faraday's Law of Electromagnetic Induction the induced voltage is equal to the rate of change of the magnetic flux. ε = ∆ φ / t ε = (7.0 T m2 - 1.0 T m^2) / 2.0 s *ε = 3.0 T m^2/ s*

A proton travels through a region of space with no acceleration. Which one of the following statements is the best conclusion?

E and B might both be non-zero, but they must be mutually perpendicular.

A coil of wire of one turn has a cross-sectional area of 0.08 m2. A magnetic field of 0.4 T passes through the coil perpendicular to the plane of the coil. What is the total magnetic flux through the coil?

For a coil positioned in a plane perpendicular to the magnetic field the flux is the product of the magnetic field times the area of the loop φ = B A *φ = (0.4 T) (0.08 m2) = 0.032 T m2*

21.1 Magnetic Fields

Surrounding a magnet there is a *magnetic field.* The magnetic field is analogous to the electric field that exists in the space around electric charges. -The direction of the magnetic field at any point in space is the direction indicated by the north pole of a small compass needle placed at that point. -has magnitude and direction (vector)

Which one of the following statements concerning permanent magnets is false? a) Magnets can exert forces on each other. b) A north pole attracts a south pole. c) There is a magnetic field surrounding a magnet. d) The north pole of a compass points toward the south pole of a permanent magnet. e) The magnetic field is directed away from a north pole and into a south pole.

The north pole of a compass points toward the south pole of a permanent magnet.

Which one of the following conditions is not a requirement for a particle to experience a magnetic force when placed in a magnetic field?

The particle must not be under the influence of any other forces.

21.6 The Torque on a Current-Carrying Coil Homework 42. Two coils have the same number of circular turns and carry the same current. Each rotates in a magnetic field as in Figure 21.19. Coil 1 has a radius of 5.0 cm and rotates in a 0.18-T field. Coil 2 rotates in a 0.42-T field. Each coil experiences the same maximum torque. What is the radius (in cm) of coil 2?

I= [r(2)^2⋅B(2)/ r(1)^2⋅B(1)] *r(2)=r(1)√[B(1)/B(2)]=* *(5.0 cm)√(0.18 T/ 0.42 T)= 3.3 cm*

Complete the following sentence: When a negatively-charged particle is moving at a constant velocity due east and enters in a region that has a magnetic field directed due east, the particle will

continue moving due east at constant velocity.

Two loops carry equal currents I in the same direction. They are held in the positions shown in the figure and project above and below the plane of the paper. The point P lies exactly halfway between them on the line that joins their centers. The centers of the loops and the point P lie in the plane of the paper. Which one of the figures below shows the position of a compass needle if the compass were placed in the plane of the paper at P?

d [horizontal n to the left]

[DOUBLE RAINBOW PIC] 23. What is the direction of the magnetic field?

into the page

21.7 Magnetic Fields Produced by Currents Homework 54. A long solenoid has a length of 0.65 m and contains 1400 turns of wire. There is a current of 4.7 A in the wire. What is the magnitude of the magnetic field within the solenoid?

*B=u()NI/L=* *(4π⋅1e-7)(1400)(4.7 A)/ 0.65 m= 1.27e-2 T*

The drawing shows two long, thin wires that carry currents in the positive z direction. Both wires are parallel to the z axis. The 50-A wire is in the x-z plane and is 5 m from the z axis. The 40-A wire is in the y-z plane and is 4 m from the z axis. What is the magnitude of the magnetic field at the origin? A) zero tesla B) 1 x 10^-6 T C) 3 x 10^-6 T D) 5 x 10^-6 T E) 7 x 10^-6 T

*C) 3 x 10^-6 T * B=(u()I/2πr) B(total)= √( B(1)² + B(2)²)= √(2e-6^2 + 2e-6^2)= 2.8e-6 T

Which one of the following statements best explains why a constant magnetic field can do no work on a moving charged particle? A) The magnetic field is conservative. B) The magnetic force is a velocity dependent force. C) The magnetic field is a vector and work is a scalar quantity. D) The magnetic force is always perpendicular to the velocity of the particle. E) The electric field associated with the particle cancels the effect of the magnetic field on the particle.

*D) The magnetic force is always perpendicular to the velocity of the particle.*

22.4 Faraday's Law of Electromagnetic Induction Check Your Understanding 7. Even without directly striking an electrical appliance in your house, a bolt of lightning that strikes nearby can produce a current in the circuits of the appliance. Note that such circuits typically contain coils or loops of wire. Why can the lightning cause the current to appear?

*Due to change in magnetic field by lightning.* Lightning carries a huge amount of current which changes with time. Current produces a magnetic field, which passes through the coils of appliances. Due to change in magnitude of current, the magnetic field magnitude also changes. The change in magnetic field through the coils of appliances produce an induced emf, which can lead to an induced current. *current->magnetic field* *△current->△magnetic field* *△magnetic field->induced emf->induced current*

CH 22 HW Section 22.2 Motional Emf 3. In 1996, NASA performed an experiment called the Tethered Satellite experiment. In this experiment a 2.0 e4 m length of wire was let out by the space shuttle Atlantis to generate a motional emf. The shuttle had an orbital speed of 7.6 × 103 m/s, and the magnitude of the earth's magnetic field at the location of the wire was 5.1e5 T. If the wire had moved perpendicular to the earth's magnetic field, what would have been the motional emf generated between the ends of the wire?

*Emf= vBL* =(7.6e3 m/s)(5.1e-5 T)(2.0e4 m) =*7800 V*

21.5 The Force on a Current in a Magnetic Field

*F=(△q/ △t)(v△t)Bsinθ=ILBsinθ* magnetic force on a current-carrying wire of length L -the direction of the force is determined in the usual manner by using RHR-1, with the minor modification that the direction of the velocity of a positive charge is replaced by the direction of the conventional current (I)

20. 2 The Force That a Magnetic Field Exerts on a Charge

*F=qE* *F=q()(vBsinθ)* conditions for a charge to experience a magnetic force when placed in a magnetic field: 1. The charge must be moving because no magnetic force acts on a stationary charge. 2. The velocity of the moving charge must have a component that is perpendicular to the direction of the magnetic field. Right Hand Rule No. 1. Extend the right hand so the fingers point along the direction of the magnetic field and the thumb points along the velocity of the charge. The palm of the hand then faces in the direction of the magnetic force that acts on a positive charge. -If the moving charge is negative, the direction of the force is opposite to that predicted by RHR-1. magnitude of magnetic field= B *B= F/ (qvsinθ)* -where the angle (0<θ<180o) is the angle between the velocity of the charge and the direction of the magnetic field SI unit= T (tesla)= N⋅s/ C⋅m 1 gauss= e-4 tesla

CH 22 HW Section 22.3 Magnetic Flux 22. The magnetic flux that passes through one turn of a 12-turn coil of wire changes to 4.0 from 9.0 Wb in a time of 0.050 s. The average induced current in the coil is 230 A. What is the resistance of the wire?

*R=emf/I* *emf= -N(△Φ/△t)* *R= [-N(△Φ/△t)/I]* =[(-12)(4.0 wB-9.0 wB/0.050s)]/230 A= *5.2 Ω*

21.7 Magnetic Fields Produced by Currents

*Right-Hand Rule No. 2* Curl the fingers of the right hand into the shape of a half circle. Point the thumb in the direction of the conventional current, and the tips of the fingers will point in the direction of the magnetic field. -A current carrying a wire also produces a magnetic field of its own. -Current carrying wires can exert forces on each other. *electromagnetism*- motion of electric charges with the creation of a magnetic field A LONG, STRAIGHT WIRE *B=(u()I/2πr)* A LOOP OF WIRE center of circular loop permeability of free space= u()= 4π⋅1e-7 T⋅m/A *F=qvBsinθ=qV(u()I/2πr)sinθ* -The field lines around the bar magnet resemble those around the loop. -A solenoid is a long coil wire in the shape of a helix. Interior of a solenoid: *B= u()nI* n= number of turns per unit length

CH 22 HW Section 22.5 Lenz's Law *32. Starting from the position indicated in the drawing, the semicircular piece of wire rotates through half a revolution in the direction shown. Which end of the resistor is positive—the left or the right end? Explain your reasoning.

*The right end resistor must be positive* As the loop rotates through one-half revolution, the area through which the magnetic field passes decreases. The magnetic flux, being proportional to the area, also decreases. The induced magnetic field must oppose this decrease in flux, so the induced magnetic field must strengthen the original magnetic field. Thus, the induced magnetic field points in the same direction as the original magnetic field. According to RHR-2, the induced current flows clockwise around the loop so that its magnetic field will be directed downwards. Since conventional current flows from a resistor with higher potential towards lower potential, the right end resistor must be positive.

20. 2 The Force That a Magnetic Field Exerts on a Charge Check Your Understanding 3. A charged particle, passing through a certain region of space, has a velocity whose magnitude and direction remain constant. a) If it is known that the external magnetic field is zero everywhere in this region, can you conclude that the external electric field is also zero? b) If it is known that the external electric field is zero everywhere, can you conclude that the external magnetic field is also zero?

*Yes, No* When the particle travels through the space, if its velocity and direction remain the same, means that the net force acting on it is zero. If the electric field is present in the region, there ought to be a force from the electric field and net force cannot be zero because there is no other source of force. Since the net force is zero, means that the net electric field is zero. If a particle has a velocity parallel to the direction of electric field, the force due to magnetic field will be zero, so if just magnetic field is present, we cannot comment anything about the magnetic field in the region

21.1 Magnetic Fields 21.2 The Force That a Magnetic Field Exerts on a Moving Charge Homework 1. In New England, the horizontal component of the earth's magnetic field has a magnitude of 1.6e−5 T. An electron is shot vertically straight up from the ground with a speed of 2.1e6 m/s. What is the magnitude of the acceleration caused by the magnetic force? Ignore the gravitational force acting on the electron.

*a= (qVBsinθ)/m=* [(1.60e-19 C)(2.1e6 m/s)(1.6e−5 T)(sin90°)]/9.11e-31 kg = *5.9e12 m/s*

22.3 Magnetic Flux Check Your Understanding 6. Suppose that a magnetic field is constant everywhere on a flat 1.0 m^2 surface and that the magnetic flux through this surface is 2.0 Wb. From these data, which one of the following pieces of information can be determined about the magnetic field?

*the magnitude of the component of the field that is perpendicular to the surface* Magnetic flux is equal to the product of the area and the component of magnetic field perpendicular to that area. Φ=BAcosθ= 2.0 Wb A= 1 m^2 Bcosθ= 2 T Bcosθ is the component of the magnetic field perpendicular to the area

22.4 Faraday's Law of Electromagnetic Induction Check Your Understanding 10. A coil is placed in a magnetic field, and the normal to the plane of the coil remains parallel to the field. Which one of the following options causes the magnitude of the average emf induced in the coil to be as large as possible? a) the magnitude of the field is small, and its rate of change is large b) the magnitude of the field is large, and its rate of change is small c) the magnitude of the field is large, and it does not change

*the magnitude of the field is small, and its rate of change is large* The induced emf is given by the product of rate of change of magnetic field and the area perpendicular to the magnetic field. *The induced emf does not depend upon the magnitude of magnetic field, but its rate of change.*

CH 22 HW Section 22.9 Transformers 60. The battery charger for an MP3 player contains a step-down transformer with a turns ratio of 1:32, so that the voltage of 120 V available at a wall socket can be used to charge the battery pack or operate the player. What voltage does the secondary coil of the transformer provide?

*v(s)= v(p)N(s)/N(p)= (120 V)(1/32)= 3.8 V*

A circular coil of wire has 25 turns and has a radius of 0.075 m. The coil is located in a variable magnetic field whose behavior is shown on the graph. At all times, the magnetic field is directed at an angle of 75° relative to the normal to the plane of a loop. What is the average emf induced in the coil in the time interval from t = 5.00 s to 7.50 s?

-18 mV

What is the magnitude of the average induced emf in the loop if the magnitude of the magnetic field is doubled in 0.4 s?

0.014 V

A long, straight wire carries a 6.0-A current that is directed in the positive x direction. When a uniform magnetic field is applied perpendicular to a 3.0-m segment of the wire, the magnetic force on the segment is 0.36 N, directed in the negative y direction, as shown. What are the magnitude and direction of the magnetic field?

0.020 T, out of the paper

A 0.0150-m wire oriented horizontally between the poles of an electromagnet carries a direct current of 9.5 A. The angle between the direction of the current and that of the magnetic field is 25.0° as shown. If the magnetic field strength is 0.845 T, what is the magnitude and direction of the magnetic force on the wire between the poles?

0.0509 N, upward

[DOUBLE RAINBOW PIC] 24. Determine the magnitude of the magnetic field if ion A travels in a semicircular path of radius 0.50 m at a speed of 5.0 × 106 m/s.

0.21 T

A 0.60-T magnetic field is directed perpendicular to the plane of a circular loop of radius 0.40 m. What is the magnitude of the magnetic flux through the loop?

0.30 Wb

A uniform magnetic field passes through two areas, A1 and A2. The angles between the magnetic field and the normals of areas A1 and A2 are 30.0° and 60.0°, respectively. If the magnetic flux through the two areas is the same, what is the ratio A1/A2?

0.354

[hockey rink w/S zamboni inside and N zamboni outside] What is the magnitude of the magnetic force acting on the wire?

0.48 N

A mass spectrometer is used to separate two isotopes of uranium with masses m1 and m2 where m2 > m1. The two types of uranium atom exit an ion source S with the same charge of +e and are accelerated through a potential difference V. The charged atoms then enter a constant, uniform magnetic field B as shown. If r1 = 0.5049 m and r2 = 0.5081 m, what is the value of the ratio m1/m2?

0.9874

What is the direction of the magnetic field at the point P, directly below a point at the center of the magnet? The numbered arrows represent various directions. Direction "1" is to the right, "2" to the left, "3" is upward, "4" is downward, and "5" is toward you.

1

The Earth's magnetic field passes through a square tabletop with a magnitude of 4.95 × 10-5 T and is directed at an angle of 165° relative to the normal of the tabletop. If the tabletop has 1.50- m sides, what is the magnitude of the magnetic flux through it?

1.08 × 10-4 Wb

A loop of wire with a weight of 0.55 N is oriented vertically and carries a current I = 2.25 A. A segment of the wire passes through a magnetic field directed into the plane of the page as shown. The net force on the wire is measured using a balance and found to be zero. What is the magnitude of the magnetic field?

1.2 T

A long straight wire carries a 40.0 A current in the +x direction. At a particular instant, an electron moving at 1.0 × 107 m/s in the +y direction is 0.10 m from the wire. The charge on the electron is -1.6 × 10-19 C. What is the force on the electron at this instant?

1.3 × 10-16 N in the +x direction

A single circular loop of radius 1.00 m carries a current of 10.0 mA. It is placed in a uniform magnetic field of magnitude 0.500 T that is directed parallel to the plane of the loop as suggested in the figure. What is the magnitude of the torque exerted on the loop by the magnetic field? [circle on 5 right pointing arrows]

1.57 × 10-2 N × m

A single circular loop of wire of radius 0.45 m carries a constant current of 2.4 A. The loop may be rotated about an axis that passes through the center and lies in the plane of the loop. When the orientation of the normal to the loop with respect to the direction of the magnetic field is 36°, the torque on the coil is 1.5 N × m. What is the magnitude of the uniform magnetic field exerting this torque on the loop?

1.7 T

A conducting loop has an area of 0.065 m2 and is positioned such that a uniform magnetic field is perpendicular to the plane of the loop. When the magnitude of the magnetic field decreases to 0.30 T in 0.087 s, the average induced emf in the loop is 1.2 V. What is the initial value of the magnetic field?

1.9 T

[horizontal road, C in center, O on sidewalk] Two long, straight, parallel wires separated by a distance d carry currents in opposite directions as shown in the figure. The bottom wire carries a current of 6.0 A. Point C is at the midpoint between the wires and point O is a distance 0.50d below the 6-A wire as suggested in the figure. The total magnetic field at point O is zero tesla. Determine the value of the current, I, in the top wire.

18 A

A charged particle is launched with a velocity of 5.2 × 104 m/s at an angle of 35° with respect to a 0.0045-T magnetic field. If the magnetic field exerts a force of 0.0026 N on the particle, determine the magnitude of the charge on the particle.

19 µC

If the magnetic field is held constant at 3.0 T and the loop is pulled out of the region that contains the field in 0.2 s, what is the magnitude of the average induced emf in the loop?

2.7 × 10-2 V

A long, coaxial cable, shown in cross-section in the drawing, is made using two conductors that share a common central axis, labeled C. The conductors are separated by an electrically insulating material that is also used as the outer cover of the cable. The current in the inner conductor is 2.0 A directed into the page and that in the outer conductor is 2.5 A directed out of the page. The distance from point C to point A is 0.0015 m; and the distance from C to B is 0.0030 m. The radii a and b of the conductors are 6.0 × 10-4 m and 1.9 × 10-3 m, respectively. What is the magnitude and direction of the magnetic field at point A? [four ringed circle]

2.7 × 10-4 T, clockwise

An electron is moving with a speed of 3.5 × 105 m/s when it encounters a magnetic field of 0.60 T. The direction of the magnetic field makes an angle of 60.0° with respect to the velocity of the electron. What is the magnitude of the magnetic force on the electron?

2.9 × 10-14 N

The drawing shows two long, thin wires that carry currents in the positive z direction. Both wires are parallel to the z axis. The 50-A wire is in the x-z plane and is 5 m from the z axis. The 40-A wire is in the y-z plane and is 4 m from the z axis. What is the magnitude of the magnetic field at the origin?

3 × 10-6 T

Determine the magnitude of the total magnetic field at the center of the loop (due both to the loop and the solenoid) if the current in the loop is reversed in direction from that needed to make the total field equal to zero tesla.

3.0 × 10-4 T

A coil consists of 240 circular loops, each of radius 0.044 m, and carries a current of 2.2 A. Determine the magnetic moment of the coil.

3.2 A × m2

What is the magnitude and direction of the magnetic field at point B? [four ringed circle]

3.3 × 10-5 T, counterclockwise

A 250-turn solenoid carries a current of 9.0 A. The radius of the solenoid is 0.075 m; and its length is 0.14 m. Determine the magnetic flux through the circular cross-sectional area at the center of the solenoid.

3.6 × 10-4 Wb

A circular coil consists of 5 loops each of diameter 1.0 m. The coil is placed in an external magnetic field of 0.5 T. When the coil carries a current of 4.0 A, a torque of magnitude 3.93 N-m acts on it. Determine the angle between the normal to the plane of the coil and the direction of the magnetic field.

30°

[vertical road, P on sidewalk] Determine the magnitude of the magnetic field at the point P.

4.8 × 10-5 T

If the magnetic field is held constant at 3.0 T and the loop is pulled out of the region that contains the field in 0.2 s, at what rate is energy dissipated in R?

4.9 × 10-4 W

Each second, 1.25 × 1019 electrons in a narrow beam pass through a small hole in a wall. The beam is perpendicular to the wall. Using Ampere's law, determine the magnitude of the magnetic field in the wall at a radius of 0.750 m from the center of the beam.

5.34 × 10-7 T

A circular copper loop is placed perpendicular to a uniform magnetic field of 0.75 T. Due to external forces, the area of the loop decreases at a rate of 7.26 × 10-3 m2/s. Determine the induced emf in the loop.

5.4 × 10-3 V

[centipede pic; current carrying loop in center] Determine the value of the current in the solenoid so that the magnetic field at the center of the loop is zero tesla.

6.0 × 10-2 A

A 1.2-kg rod that has a length of 1.0 m and a resistance of 5.0 slides with constant speed down a pair of frictionless vertical conducting rails that are joined at the bottom. Other than the rod, the rest of the circuit is resistanceless. A uniform magnetic field of magnitude 3.0 T is perpendicular to the plane formed by the rod and the rails as shown. Determine the speed of the rod.

6.5 m/s

A magnetic field is directed perpendicular to the plane of a 0.15-m × 0.30-m rectangular coil consisting of 240 loops of wire. To induce an average emf of -2.5 V in the coil, the magnetic field is increased from 0.1 T to 1.8 T during a time interval t. Determine t.

7.3 s

A particle with a mass of 6.64 × 10-27 kg and a charge of +3.20 × 10-19 C is accelerated from rest through a potential difference of 2.45 × 106 V. The particle then enters a uniform 1.60-T magnetic field. If the particle's velocity is perpendicular to the magnetic field at all times, what is the magnitude of the magnetic force exerted on the particle?

7.87 × 10-12 N

The radius of a coil of wire with N turns is r = 0.28 m. A clockwise current of Icoil = 1.0 A flows in the coil, as shown. A long, straight wire carrying a current I wire = 29 A toward the left is located 0.04 m from the edge of the coil. The magnetic field at the center of the coil is zero tesla. Determine N, the number of turns.

8

A rectangular loop has sides of length 0.06 m and 0.08 m. The wire carries a current of 10 A in the direction shown. The loop is in a uniform magnetic field of magnitude 0.2 T and directed in the positive x direction. What is the magnitude of the torque on the loop?

8 × 10-3 N × m

What is the average current around the loop if the magnitude of the magnetic field is doubled in 0.4 s?

9.0 × 10-3 A, clockwise

[horizontal road, C in center, O on sidewalk] Determine the magnitude of the magnetic field at point C if d = 0.10 m.

9.6 × 10-5 T

Which of the following units are equivalent to those of motional emf?

A * Ohm

Which one of the following statements concerning transformers is false?

A transformer can function with either an ac current or a steady dc current.

Suppose that the radius of the loop is 0.500 m. At what rate must B change with time if the emf induced in the loop is 3 volts? A) 12.0 T/s B) 18.8 T/s C) 24.0 T/s D) 37.7 T/s E) 49.2 T/s

A) 12.0 T/s

A small power plant produces a voltage of 6.0 kV and 150 A. The voltage is stepped up to 240 kV by a transformer before it is transmitted to a substation. The resistance of the transmission line between the power plant and the substation is 75 . What is the current in the transmission line from the plant to the substation? A) 3.8 A B) 5.2 A C) 6.4 A D) 7.0 A E) 7.5 A

A) 3.8 A

A coil of wire with a resistance of 0.45 has a self-inductance of 0.083 H. If a 6.0-V battery is connected across the ends of the coil and the current in the circuit reaches an equilibrium value, what is the stored energy in the inductor? A) 7.4 J B) 4.6 J C) 1.6 J D) 5.1 J E) 3.4 J

A) 7.4 J

Immediately after the switch S is closed, which one of the following statements is true? A) An induced current will flow from right to left in R. B) An induced current will flow from left to right in r. C) A magnetic field that points toward B appears inside coil 1. D) An induced magnetic field that points toward B appears inside coil 2. E) A current will pass through r, but there will be no current through R.

A) An induced current will flow from right to left in R.

Two parallel wires with the same current i exert forces on each other with equal magnitudes. What happens to the magnitude of this force if the current is halved?

A) The magnitude is quartered The magnitude of force F on a current carrying wire of length L is given by F = L i B , i is the current in the wire , B is the magnetic field produced by the second wire. The magnitude of the magnetic field B due to a current carrying wire (second wire) is given by B = μ0 i / (2 π r) , Substitute B in F by the expression μ0 i / (2 π r) F = L B μ0 i2 / (2 π r) If you replace i by i/2 (half) then the new force is 1/4 of the force with current i.

The current in a solenoid is decreased to one-half of its original value. Which one of the following statements is true concerning the self-inductance of the solenoid? A) The self-inductance does not change. B) The self-inductance increases by a factor of two. C) The self-inductance decreases by a factor of two. D) The self-inductance increases by a factor of four. E) The self-inductance decreases by a factor of four.

A) The self-inductance does not change.

Assume that S has been closed for a long time. Which one of the following statements is true if coil 2 is moved toward C? A) There is an induced magnetic field in coil 2 that points toward B. B) There is an induced magnetic field in coil 2 that points toward C. C) There is an induced current in R that flows from right to left. D) There is an induced north pole at the right end of coil 2. E) There is no induced current in R.

A) There is an induced magnetic field in coil 2 that points toward B.

The figure shows a circular, conducting loop that is connected to a 5.0-V battery and a switch S. Immediately after the switch S is closed, the current through the loop changes at a rate of 15 A/s and the emf induced in the loop has a magnitude of 5.0 V. Determine the self- inductance of the coil. A. 0.33 H B. 0.60 H C. 1.5 H D. 3.0 H E. 5.0 H

A. 0.33 H

Two long bar magnets, positioned on a table with their north poles facing each other, exert a force of 5.0 N on each other. If the distance between these two poles is doubled what is the new value of the force between them?

According to Coulomb's Law for Magnetism, the force between magnetic poles is an inverse square law. Thus if the distance between the poles is doubled the force is changed by a factor of 1 / r2 or, in this case, by a factor of 1 / (2 )2 = 1 / 4. Doubling the separation distance *reduces the force to one-fourth its original value.*

21.8 Ampere's Law

Ampere's law- specifies the relationship between an electric current and the magnetic field it creates For any current geometry that produces a magnetic field that does not change in time, *ΣB△l=u()I= B(Σ△l)=u()I= B2πr/ u()I* where B is the component of the magnetic field that is parallel to △l *B=u()I/2πr* I= net current passing through surface bounded by path

A metal ring is dropped from rest below a bar magnet that is fixed in position as suggested in the figure. An observer views the ring from below. Which one of the following statements concerning this situation is true?

As the ring falls, an induced current will flow counterclockwise as viewed by the observer.

A beam consisting of five types of ions labeled A, B, C, D, and E enters a region that contains a uniform magnetic field as shown in the figure below. The field is perpendicular to the plane of the paper, but its precise direction is not given. All ions in the beam travel with the same speed. The table below gives the masses and charges of the ions. Note: 1 mass unit = 1.67 × 10-27 kg and e = 1.6 × 10-19 C [DOUBLE RAINBOW PIC] Which ion falls at position 2?

B

A loop is pulled with a force F to the right to maintain a constant speed of 8.0 m/s. The loop has a length of 0.15 m, a width of 0.080 m, and a resistance of 200.0 . At the instant shown, the loop is partially in and partially out of a uniform magnetic field that is directed into the paper. The magnitude of the field is 1.2 T. 61. What is the magnitude of the emf induced in the loop? A) zero volts B) 0.77 V C) 1.4 V D) 4.9 V E) 9.6 V

B) 0.77 V

Determine the induced emf in the loop. A) 0.7 × 10-3 V B) 1.4 × 10-3 V C) 2.8 × 10-3 V D) 5.6 × 10-3 V E) zero volts

B) 1.4 × 10-3 V

Determine the mutual inductance of this combination. A) 1.8 × 10-4 H B) 2.4 × 10-4 H C) 3.6 × 10-4 H D) 4.4 × 10-4 H E) 5.9 × 10-4 H

B) 2.4 × 10-4 H

Determine the magnitude of the induced current through the resistor. A) 2.0 A B) 3.5 A C) 4.6 A D) 7.2 A E) 11 A

B) 3.5 A

Determine the magnitude of the uniform magnetic field. A) 2.2 T B) 3.5 T C) 6.4 T D) 7.0 T E) 9.1 T

B) 3.5 T

What is the magnitude of v? A) 1.5 m/s B) 4.6 m/s C) 6.4 m/s D) 7.8 m/s E) 9.0 m/s

B) 4.6 m/s

The angular speed of a motor is 262 rad/s. The back emf generated by the motor is 89.4 V. Assuming all other factors remain the same, determine the back emf if the angular speed of the motor is reduced to 131 rad/s. A) 32.3 V B) 44.7 V C) 52.5 V D) 89.4 V E) 152 V

B) 44.7 V

At what rate is heat generated in the loop? A) 3.6 × 10-3 W B) 8.7 × 10-4 W C) 8.7 × 104 W D) 8.1 × 105 W E) 8.1 × 10-5 W

B) 8.7 × 10-4 W

A transformer changes 120 V across the primary to 1200 V across the secondary. If the secondary coil has 800 turns, how many turns does the primary coil have? A) 40 B) 80 C) 100 D) 400 E) 4000

B) 80

Assume that S has been closed for a long time. Which one of the following changes will not result in an induced current in coil 2 that flows from left to right through R. A) Coil 1 and its core are moved toward A. B) Coil 2 and its core are moved toward B. C) Coil 2 and its core are moved toward C. D) The switch S is opened. E) The iron core is removed from coil 1.

B) Coil 2 and its core are moved toward B.

A long, straight wire is in the same plane as a wooden, non-conducting loop. The wire carries an increasing current I in the direction shown in the figure. A. There will be no induced emf and no induced current. B. There will be a counterclockwise induced emf, but no induced current. C. There will be a clockwise induced emf, but no induced current. D. There will be a clockwise induced current in the loop. E. There will be a counterclockwise induced current in the loop.

B. There will be a counterclockwise induced emf, but no induced current.

A long, straight wire carries a current I. If the magnetic field at a distance d from the wire has magnitude B, what is the magnitude of the magnetic field at a distance 2d from the wire?

B/2

21.7 Magnetic Fields Produced by Currents Example 10 Finding the Net Magnetic Field A long straight wire carries a current of 8.0 A and a circular loop of wire carries a current of 2.0 A and has a radius of 0.030 m. Find the magnitude and direction of the magnetic field at the center of the loop.

B=(u()I(1)/2πr)-(u()I(2)/2πr)= *(u()/2)⋅(I(1)/πr - I(2)/ R)=* *(4π⋅1e-7 T⋅m/A/2)([8.0 A/ π(0.030 m)]- 2.0 A/* *0.030 m)= 1.1e-5 T*

The current in the secondary coil of a step-up transformer is 1.25 A when the current in the primary coil is 0.30 A. Determine the turns ratio, Ns/Np, of the transformer. A) 5.6 B) 4.2 C) 0.24 D) 0.18 E) 0.12

C) 0.24

Determine the self-induced emf in the solenoid due to the changing current. A) 60 V B) 98 V C) 130 V D) 180 V E) 250 V

C) 130 V

Determine the strength of the magnetic field in which the loop rotates. A) 0.5 T B) 2.4 T C) 3.0 T D) 7.5 T E) 18.8 T

C) 3.0 T

Determine the magnitude of the force required to pull the loop. A) 1.3 × 10-4 N B) 2.1 × 10-4 N C) 3.7 × 10-4 N D) 6.8 × 10-4 N E) 9.0 × 10-4 N

C) 3.7 × 10-4 N

In the drawing, a coil of wire is wrapped around a cylinder from which an iron core extends upward. The ends of the coil are connected to an ac voltage source. After the alternating current is established in the coil, an aluminum ring of resistance R is placed onto the iron core and released. Which one of the following statements concerning this situation is false? A) The induced current in the ring is an alternating current. B) The temperature of the ring will increase. C) At any instant, the direction of the induced current in the ring is in the same direction as that in the coil. D) The induced magnetic field in the ring may by directed either upward or downward at an instant when the direction of the magnetic field generated by the current in the coil is upward. E) The ring may remain suspended at the position shown with no vertical movement of its center of mass.

C) At any instant, the direction of the induced current in the ring is in the same direction as that in the coil.

Which one of the following phrases best describes the direction of the induced magnetic field generated by the current induced in the loop while the loop is being stretched? A) clockwise B) counterclockwise C) into the page D) out of the page E) The induced field is zero.

C) into the page

A closed loop carries a current that increases with time. Which one of the quantities listed below relates the emf induced in the loop to the rate at which the current is increasing? A) resistance of the loop B) capacitance of the loop C) self-inductance of the loop D) power dissipated by the loop E) mutual inductance of the loop

C) self-inductance of the loop

A solenoid with 1000 turns has a cross-sectional area of 7.0 cm2 and length of 25 cm. How much energy is stored in the magnetic field of the solenoid when it carries a current of 10.0 A? A. 0.10 J B. 2.8 J C. 0.18 J D. 28 J E. 0.36 J

C. 0.18 J

Which one of the following statements concerning transformers is false? A. Their operation makes use of mutual induction. B. They are an application of Faraday's and Lenz's laws. C. A transformer can function with either an ac current or a steady dc current. D. A transformer that steps down the voltage, steps up the current. E. A transformer that steps up the voltage, steps down the current.

C. A transformer can function with either an ac current or a steady dc current.

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Cptr 22

Determine the magnitude of the induced emf in the loop. A) 2.0 V B) 4.0 V C) 8.0 V D) 14 V E) 16 V

D) 14 V

What is the induced current in the loop? A) 0.048 A B) 0.024 A C) 7.2 × 10-3 A D) 3.8 × 10-3 A E) zero amperes

D) 3.8 × 10-3 A

At what rate is energy dissipated by the resistor? A) 130 W B) 96 W C) 32 W D) 49 W E) 8.0 W

D) 49 W

What is the period of the induced current? A) 1.25 s B) 2.50 s C) 3.75 s D) 5.00 s E) 6.25 s

D) 5.00 s

A flexible, circular conducting loop of radius 0.15 m and resistance 4.0 lies in a uniform magnetic field of 0.25 T. The loop is pulled on opposite sides by equal forces and stretched until its enclosed area is essentially zero m2, as suggested in the drawings. It takes 0.30 s to close the loop. Determine the magnitude of the emf induced in the loop. A) 1.2 × 10-1 V B) 1.8 × 10-2 V C) 1.8 × 102 V D) 5.9 × 10-2 V E) 5.9 × 102 V

D) 5.9 × 10-2 V

Determine the energy stored in a 7.09 × 10-7 H inductor that carries a 1.50-A current. A) 2.11 × 10-8 J B) 3.78 × 10-8 J C) 1.09 × 10-7 J D) 7.98 × 10-7 J E) 6.60 × 10-6 J

D) 7.98 × 10-7 J

Assume S has been closed for a long time. Which one of the following statements is true when coil 1 and its core are moved toward point B? A) There is no induced current in r. B) There is a magnetic field in coil 1 that points toward B. C) There is an induced current in R that flows from left to right. D) There is an induced current in R that flows from right to left. E) There is an induced magnetic field in coil 2 that points toward B.

D) There is an induced current in R that flows from right to left.

A loop with a resistance of 4.0 is pushed to the left at a constant speed of 2.0 m/s by a 24 N force. At the instant shown in the figure, the loop is partially in and partially out of a uniform magnetic field. An induced current flows from left to right through the resistor. The length and width of the loop are 2.0 m and 1.0 m, respectively. What is the direction of the magnetic field? A) to the left B) to the right C) out of the paper D) into the paper E) toward the top of the page

D) into the paper

A circular coil has 275 turns and a radius of 0.045 m. The coil is used as an ac generator by rotating it in a 0.500 T magnetic field, as shown in the figure. At what angular speed should the coil be rotated so that the maximum emf is 175 V? A. 28 rad/s B. 50 rad/s C. 130 rad/s D. 200 rad/s E. 490 rad/s

D. 200 rad/s

Assume that S has been closed for a long time. Which one of the following changes will result in an induced magnetic field in coil 2 that points toward C? A. The switch S is opened. B. The iron core is removed from coil 1. C. Coil 1 and its core are moved toward A. D. Coil 1 and its core are moved toward B. E. Coil 2 and its core are moved toward C.

D. Coil 1 and its core are moved toward

A sheet of copper is pulled at constant velocity v from a region that contains a uniform magnetic field. At the instant shown in the figure, the sheet is partially in and partially out of the field. The induced emf in the sheet leads to the eddy current shown. Which one of the following statements concerning the direction of the magnetic field is true? A. The magnetic field points to the right. B. The magnetic field points to the left. C. The magnetic field points into the paper. D. The magnetic field points out of the paper. E. The direction of the magnetic field cannot be determined from the information given.

D. The magnetic field points out of the pape

What percentage of the power produced at the power plant is lost in transmission to the substation? A) 0.47 % B) 0.41 % C) 0.34 % D) 0.23 % E) 0.12 %

E) 0.12 %

A single conducting loop with an area of 2.0 m2 rotates in a uniform magnetic field so that the induced emf has a sinusoidal time dependence as shown. 28. With what angular frequency does the loop rotate? A) 0.16 rad/s B) 0.30 rad/s C) 0.52 rad/s D) 0.80 rad/s E) 1.26 rad/s

E) 1.26 rad/s

A 0.100-m long solenoid has a radius of 0.050 m and 1.50 × 104 turns. The current in the solenoid changes at a rate of 6.0 A/s. A conducting loop of radius 0.0200 m is placed at the center of the solenoid with its axis the same as that of the solenoid as shown. 39. What is the magnetic flux through the small loop when the current through the solenoid is 2.50 A? A) 2.95 × 10-2 Wb B) 7.28 × 10-2 Wb C) 2.95 × 10-4 Wb D) 4.38 × 10-4 Wb E) 5.92 × 10-4 Wb

E) 5.92 × 10-4 Wb

A circular loop of copper wire with an area of 2.0 m2 lies in a plane perpendicular to a time- dependent magnetic field oriented as shown. The time-dependence of the field is shown in the graph. Which one of the entries in the table below is incorrect? Time, Induced emf A)1s, zero volts B) 4s, 2.5 V, counterclockwise C) 5s, 2.5 V, counterclockwise D) 7s, 10 V, clockwise E) 9s, 10 V, counterclockwise

E) 9s, 10 V, counterclockwise

Assume the switch S has been closed for a long time. Which one of the following statements is true? A) An induced current will flow from right to left in R. B) An induced current will flow from left to right in r. C) A magnetic field that points toward B appears inside coil 1. D) An induced magnetic field that points toward B appears inside coil 2. E) A current will pass through r, but there will be no current through R

E) A current will pass through r, but there will be no current through R

In the circuit below wire PQ, with mass of 10 grams and length of 20 cm, can move up and down with negligible friction. If a uniform magnetic field B of magnitude 1 T and direction out of the page, is applied to wire PQ, what must be the direction and the smallest intensity of the current in the circuit that lifts wire PQ upward?

E) Direction: from Q to P , Minimum intensity: 0.5 A The magnetic field exerts a force F on the current carrying wire PQ. For force F to lift the wire, F must be directed upward and its magnitude greater than the weight of the wire since frictions are negligible. Using the right hand rule with middle finger in the direction of B (out of the page) and the thumb in the direction of the force (up), the index is directed from right to left which gives the direction of the current (in the moving wire) from Q to P. The magnitude of force F on a current carrying wire PQ is given by F = L i B = (0.2 m) i (1 T) F > m g , m is the mass of the wire and g = 10 m/s2 is the gravitational acceleration 0.2 i > (0.01 Kg) (10 m/s2) i > 0.5 A

Which one of the following combinations of units is equivalent to one henry? A) N m s/C B) N m s2/C C) N m C2/s2 D) N m C/s2 E) N m s2/C2

E) N m s2/C2

A transformer has 450 turns in its primary coil and 30 turns in its secondary coil. Which one of the following statements concerning this transformer is true? A) This is a step-up transformer. B) The turns ratio is 15 for this transformer. C) The ratio of the voltages Vs / Vp is 15 for this transformer. D) The ratio of the currents Is / Ip is 0.067 for this transformer. E) The power delivered to the secondary must be the same as that delivered to the primary.

E) The power delivered to the secondary must be the same as that delivered to the primary.

Assume that S has been closed for a long time. Which one of the following statements is true if S is suddenly opened? A) There is no induced current through R. B) There is no induced magnetic field in coil 2. C) There is an induced current in R that flows from right to left. D) There is an induced magnetic field in coil 2 that points toward C. E) There is an induced magnetic field in coil 2 that points toward B.

E) There is an induced magnetic field in coil 2 that points toward B.

Determine the induced emf in the loop if the loop is oriented so that its axis is perpendicular to the axis of the solenoid, instead of parallel. A) 0.7 × 10-4 V B) 1.4 × 10-4 V C) 2.8 × 10-4 V D) 5.6 × 10-4 V E) zero volts

E) zero volts

Two coils share a common axis as shown in the figure. The mutual inductance of this pair of coils is 6.0 mH. If the current in coil 1 is changing at the rate of 3.5 A/s, what is the magnitude of the emf generated in coil 2? A. 5.8 × 10-4 V B. 1.7 × 10-3 V C. 3.5 × 10-3 V D. 1.5 × 10-2 V E. 2.1 × 10-2 V

E. 2.1 × 10-2 V

The figure shows a uniform magnetic field that is normal to the plane of a conducting loop with resistance R. Which one of the following changes will cause an induced current to flow through the resistor? A. decreasing the area of the loop B. decreasing the magnitude of the magnetic field C. increasing the magnitude of the magnetic field D. rotating the loop through 90° about an axis in the plane of the paper E. all of the above

E. all of the above

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Exam Flash Chapter 21

21.5 The Force on a Current in a Magnetic Field Homework 32. A straight wire in a magnetic field experiences a force of 0.030 N when the current in the wire is 2.7 A. The current in the wire is changed, and the wire experiences a force of 0.047 N as a result. What is the new current?

F(1)= I(1)LBsinθ and F(2)= I(2)LBsinθ F(2)/F(1)= [I(2)LBsinθ/I(1)LBsinθ]= I(2)/I(1) or *I(2)= I(1)⋅[F(2)/F(1)]=* *(2.7 A) (.047 N/ .030 N)= 4.2 A*

21.3 The Motion of a Charged Particle in a Magnetic Field 21.4 The Mass Spectrometer Homework 12. An ionized helium atom has a mass of 6.6e−27 kg and a speed of 4.4e5 m/s. It moves perpendicular to a 0.75-T magnetic field on a circular path that has a 0.012-m radius. Determine whether the charge of the ionized atom is +e or +2e

F= qVB= ma= (mv)^2/ r *q=(mv)/(BR)=* *(6.6e−27 kg⋅4.4e5 m/s)/(0.75-T⋅0.012-m)=* *2e=2(1.60e-19 C)* the charge of the ionized helium atom is *+2e*

Two rods are resting on a table. Although they appear to be identical, one is a permanent magnet and the other is made from soft iron and is not permanently magnetized. Which one of the following methods is most likely to reveal which rod is the magnet and which is the soft iron?

Move a compass along each rod to see if the compass needle behaves as it should in a magnetic field.

CH 22 HW Section 22.8 Mutual Inductance and Self-Inductance *53. Mutual induction can be used as the basis for a metal detector. A typical setup uses two large coils that are parallel to each other and have a common axis. Because of mutual induction, the ac generator connected to the primary coil causes an emf of 0.46 V to be induced in the secondary coil. When someone without metal objects walks through the coils, the mutual inductance and, thus, the induced emf do not change much. But when a person carrying a handgun walks through, the mutual inductance increases. The change in emf can be used to trigger an alarm. If the mutual inductance increases by a factor of three, find the new value of the induced emf.

New emf= 3(0.46 V)= *1.4 V* The induced emf in the secondary coil is proportional to the mutual inductance. If the primary coil is assumed to be unaffected by the metal, that is △I/△t is the same for both cases then.

20. 2 The Force That a Magnetic Field Exerts on a Charge Check Your Understanding 1. Suppose that you accidentally use your left hand, instead of your right one, to determine the direction of the magnetic force that acts on a positive charge moving in a magnetic field. Do you get the correct answer?

No, because the direction you get will be opposite to the correct direction

A conducting loop of wire is placed in a magnetic field that is normal to the plane of the loop. Which one of the following actions will not result in an induced current in the loop?

Rotate the loop about an axis that is parallel to the field and passes through the center of the loop.

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SAT Solutions to SAT Physics Practice Questions on Magnetism

Two conducting loops carry equal currents I in the same direction as shown in the figure. If the current in the upper loop suddenly drops to zero, what will happen to the current in the lower loop according to Lenz's law?

The current in the lower loop will increase.

Consider the two rectangular areas shown with a point P located at the midpoint between the two areas. The rectangular area on the left contains a bar magnet with the south pole near point P. The rectangle on the right is initially empty. How will the magnetic field at P change, if at all, when a second bar magnet is placed on the right rectangle with its northpole near point P?

The direction of the magnetic field will not change, but its magnitude will increase.

A circuit is pulled with a 21-N force toward the right to maintain a constant speed v. At the instant shown, the loop is partially in and partially out of a uniform magnetic field that is directed into the paper. As the circuit moves, a 4.0-A current flows through a 6.0- resistor.

The induced current flows clockwise around the circuit.

Two loops carry equal currents I in the same direction. The loops are held in the positions shown in the figure and are then released. Which one of the following statements correctly describes the subsequent behavior of the loops?

The loops attract each other.

Consider the two rectangular areas shown with a point P located at the midpoint between the two areas. The rectangular area on the left contains a bar magnet with the south pole near point P. The rectangle on the right is initially empty. How will the magnetic field at P change, if at all, when a second bar magnet is placed on the right rectangle with its southpole near point P?

The magnetic field at P will be zero tesla.

Which one of the following statements concerning the magnetic field inside (far from the surface) a long, current-carrying solenoid is true?

The magnetic field is non-zero and nearly uniform.

Which one of the following statements concerning the magnetic force on a charged particle in a magnetic field is true?

The magnetic force depends on the component of the particle's velocity that is perpendicular to the field.

A charged particle is moving in a uniform, constant magnetic field. Which one of the following statements concerning the magnetic force exerted on the particle is false?

The magnetic force increases the speed of the particle

Which one of the following statements best explains why a constant magnetic field can do no work on a moving charged particle?

The magnetic force is always perpendicular to the velocity of the particle.

A step-down transformer in a door bell is used to convert 120 Volts a.c. to 12 Volts a.c. If the primary coil has 300 turns, how many turns must the secondary coil have?

The ratio of the voltage in the secondary of a transformer to the voltage in the primary is the same as the ratio of the number of turns in the secondary to the number of turns in the primary. V2 / V1 = N2 / N1 Multiplying both sides of the equation by N1 gives us N2, the number of turns in the secondary. N2 = (V2 / V1) N1 N2 = (12 V / 120 V) (300 turns) *N2 = 30 turns* Thus a step-down transformer has fewer turns on its secondary than on its primary.

A long, straight wire is in the same plane as a rectangular, conducting loop. The wire carries a constant current I as shown in the figure. Which one of the following statements is true if the wire is suddenly moved toward the loop?

There will be an induced current that is counterclockwise around the loop.

A 0.45-m metal rod moves 0.11 m in a direction that is perpendicular to a 0.80-T magnetic field in an elapsed time of 0.036 s. Assuming that the acceleration of the rod is zero m/s2, determine the emf that exists between the ends of the rod.

This cannot be determined without knowing the orientation of the rod relative to the magnetic field.

20. 2 The Force That a Magnetic Field Exerts on a Charge Example 1 Magnetic Forces on Charged Particles A proton in a particle accelerator has a speed of 5.0e6 m/s. The proton encounters a magnetic field whose magnitude is 0.40 T and whose direction makes and angle of 30.0 degrees with respect to the proton's velocity (see part (c) of the figure). Find (a) the magnitude and direction of the force on the proton and (b) the acceleration of the proton. (c) What would be the force and acceleration of the particle were an electron?

a) *F=q()(vBsinθ)=* *(1.60e-19 C)(5.0e6 m/s)(0.40 T)(sin30°)=1.6e-13 N* the acceleration is in the direction of the force b) *a=F/m= 1.6e-13 N/ 1.67e-27 kg= 9.6e13 m/s^2* c) *a=F/m= 1.6e-13 N/ 9.11e-31 kg= 1.8e-27 m/s^2* the magnitude of the force is the same, but the direction is the opposite

21.6 The Torque on a Current-Carrying Coil Example 6 The Torque Exerted on a Current-Carrying Coil A coil of wire has an area of 2.0e-4 m^2, consists of 100 loops or turns, and contains a current of 0.045 A. The coil is placed in a uniform magnetic field of magnitude 0.15 T. (a) Determine the magnetic moment of the coil. (b)Find the maximum torque that the magnetic field can exert on the coil.

a) *NIA= (100)(0.045 A)(2.0e-4 m^2)= 9.0e-4 A⋅m^2* b)*τ= NIAB(sinθ)= (9.0e-4 Am^2)(0.15 T)(sin90°)=* *1.4e-4 N⋅m*

A long, straight wire carries a 10.0-A current in the +y direction as shown in the figure. Next to the wire is a square copper loop that carries a 2.00-A current as shown. The length of each side of the square is 1.00 m. [figure is a box!] a) What is the magnitude of the net magnetic force that acts on the loop? b) What is the direction of the net magnetic force that acts on the loop?

a) 1.7 × 10-5 N b) -x direction

An electron enters a region that contains a magnetic field directed into the page as shown [square 5x5 e enters bottom left at 30]. The velocity vector of the electron makes an angle of 30° with the +y axis. What is the direction of the magnetic force on the electron when it enters the field?

at an angle of 30° below the positive x axis

What is Right-Hand Rule #1 used to determine?

b) Given the directions of the magnetic field and magnetic force on a charged particle, it is used to determine the magnitude and sign of charge on the particle.c) Given the magnitude and sign of the charge on a particle and the direction of the magnetic force, it is used to determine the net force on the particle.

A coil of wire carries current I as shown in the figure. If the observer could "see" the magnetic field inside this arrangement of loops, how would it appear?

c [has x's in center]

For delivery of electrical power to a customer, a power-supply company decided to use a step-up (100:1) transformer. This would roughly

decrease power losses in transmission lines by 10000

A positively charged particle moves at a velocity v perpendicular to a magnetic field B. If the magnitude of the velocity v is doubled, then the magnitude of the force F acting on the moving charge is

doubled

An electron traveling due north enters a region that contains a uniform magnetic field that points due east. In which direction will the electron be deflected?

down

An electron traveling due south enters a region that contains both a magnetic field and an electric field. The electric field lines point due west. It is observed that the electron continues to travel in a straight line due south. In which direction must the magnetic field lines point?

down

An electron traveling horizontally enters a region where a uniform magnetic field is directed into the plane of the paper as shown [square 5x4 e enters top left]. Which one of the following phrases most accurately describes the motion of the electron once it has entered the field?

downward and circular

Two electrons are located in a region of space where the magnetic field is zero. Electron A is at rest; and electron B is moving westward with a constant velocity. A non-zero magnetic field directed eastward is then applied to the region. In what direction, if any, will each electron be moving after the field is applied?

electron A at rest, electron B westward

A wire is bent into the shape of a circle of radius r = 0.10 m and carries a 20.0-A current in the direction shown. [current flows clockwise] What is the direction of the magnetic field at the center of the loop?

into the plane of the paper

Which combination of units can be used to express the magnetic field?

kg/(C × s)

21.4 The Mass Spectrometer

mass spectrometers are used to determine the relative masses and abundances of isotopes (atoms which have nuclei with same number of protons but different number of neutrons) *m=(er^2/2V)B^2* *v=√(2eV/m)* in terms of potential difference *r=mV/eB* e=magnitude of electron charge KE=PE *1/2mv^2=eV*

A conducting bar moves to the left at a constant speed v on two conducting rails joined at the left as shown. As a result of the bar moving through a constant magnetic field, a current I is induced in the indicated direction. Which one of the following directions is that of the magnetic field?

out of the page

Two long wires are perpendicular to the plane of the paper as shown in the figure below. Each wire carries a current of magnitude I. The currents are directed out of the paper toward you. Which one of the following expressions correctly gives the magnitude of the total magnetic field at the origin of the (x,y) coordinate system?

u()I/√(2πd)

A proton traveling due north enters a region that contains both a magnetic field and an electric field. The electric field lines point due west. It is observed that the proton continues to travel in a straight line due north. In which direction must the magnetic field lines point?

up

A proton is traveling south as it enters a region that contains a magnetic field. The proton is deflected downward toward the earth. What is the direction of the magnetic field?

west

Two charged particles of equal mass are traveling in circular orbits in a region of uniform, constant magnetic field as shown. The particles are observed to move in circular paths of radii R1 and R2 with speeds v1 and v2, respectively.

|v1/Q1| < |v2/Q2|

CH 22 HW Section 22.3 Magnetic Flux 11. The drawing shows two surfaces that have the same area. A uniform magnetic field B fills the space occupied by these surfaces, and it is oriented parallel to the yz plane as shown. Find the ratio Φxz/Φxy of the magnetic fluxes that pass through the surfaces.

Φ= BAcosθ 90°-35°= 55° Φ(xz)/Φ(xy)=BAcosθ(xz)/BAcosθ(xy)= *cos55°/cos35°= 0.70*

21.9 Magnetic Materials

-The intrinsic "spin" and orbital motion of electrons gives rise to the magnetic properties of materials. -In *ferromagnetic materials* groups of neighboring atoms, forming *magnetic domains*, the spins of electrons are naturally aligned with each other.

21.6 The Torque on a Current-Carrying Coil

-The loop tends to rotate such that its normal becomes aligned with the magnetic field. net torque= *τ= ILB(1/2wsinθ) + ILB(1/2wsinθ= IAB(sinθ)* *τ= NIAB(sinθ)* NIA= magnetic moment

A solenoid of length 0.250 m and radius 0.0250 m is comprised of 440 turns of wire. Determine the magnitude of the magnetic field at the center of the solenoid when it carries a current of 12.0 A.

2.21 × 10-3 T

A long, straight wire is carrying a current of 5.0 A in the direction shown in the figure. The point P is 0.040 m from the wire. What is the magnitude of the magnetic field at the point P?

2.5 × 10-5 T

Four long, straight wires are parallel to each other; and their cross-section forms a square. Each side of the square is 0.020 m as shown in the figure. If each wire carries a current of 8.0 A in the direction shown in the figure, determine the magnitude of the total magnetic field at P, the center of the square.

5.3 A

An overhead electric power line carries a maximum current of 125 A. What is the magnitude of the maximum magnetic field at a point 4.50 m directly below the power line?

5.56 × 10-6 T

How is the direction of a magnetic field at a location indicated?

A magnetic field is always directed in the direction that the north pole of a small compass needle points at the location.

20. 2 The Force That a Magnetic Field Exerts on a Charge Check Your Understanding 2. Two particles, having the same charge but different velocities, are moving in a constant magnetic field. Which particle, if either, experiences the greater magnetic force?

Both particles experience the same magnetic force, because the component of each velocity that is perpendicular to the magnetic field is the same.

21.3 The Motion of a Charged Particle in a Magnetic Field

Charged particle in an electric field: *The electric force that acts on a positive charge is parallel to the electric field.* Charged particle in a magnetic field: *The magnetic force is perpendicular to both the magnetic field and the velocity.* *p.585* -The electrical force can do work on a charged particle since it can displace the particle in the direction of the force and thus change its kinetic energy. -The magnetic force cannot do work on a charged particle since it acts perpendicular to the motion of the particle so that no displacement occurs along the direction of the force and thus its speed remains constant and its kinetic energy does not change. -Since the magnetic force always remains perpendicular to the velocity, if a charged particle moves perpendicular to a uniform B-field its path will be circular. -The magnetic force always remains perpendicular to the velocity and is directed toward the center of the circular path. *F(c)=m(v^2/r)=* *qVB=m(v^2/r)=* *r=(mv)/(qV)*

In the diagram below, wire PQ is part of the closed circuit and is in a magnetic field B. If we neglect the resistance of the wires and the internal resistance of the battery, which of the following is true about the magnitude of the force acting on the wire PQ? (I) It is proportional to the magnitude of the magnetic field B (II) It is inversely proportional to R (III) It is inversely proportional to E

D) (I) and (II) only The magnitude of force F on a current carrying wire PQ is given by F = L i B , i is the current in the circuit. i = E / R Hence F = L E B / R F is proportional to L, E and B and inversely proportional to R

What is the direction of the force acting on a negatively charged particle moving from East to West in a magnetic field directed downward?

D) directed into the page

Two charged particles are traveling in circular orbits with the same speed in a region of uniform magnetic field that is directed into the page, as shown. The magnitude of the charge on each particle is identical, but the signs of the charges are unequal.

M1 > m2 Sign of charge Q1- Sign of charge Q2+

Two particles move through a uniform magnetic field that is directed out of the plane of the page. The figure shows the paths taken by the two particles as they move through the field. The particles are not subject to any other forces or fields. Which one of the following statements concerning these particles is true? [two semi circles, top left and bottom right corners]

Particle 1 is negatively charged; 2 is negative

The direction of the velocity of the particle in the previous problem is toward the top of this page and the direction of the magnetic field strength is into the page. Find the direction of the magnetic force on the particle.

Point the index finger of your right hand toward the top of the page, extend the second finger of your right hand to be perpendicular to the palm of your right hand and point it into the page. Your thumb now will point to the left, indicating that the force on the particle will be toward the left.

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Practice Problems

If a magnetic field B exerts a force F on a wire of length L with electric current in a magnetic field, then what value of the angle between the direction of the current i and the magnetic field B gives a maximum value for the magnitude of F?

The force F exerted on a wire in a magnetic field is given by F = L i × B (cross product of vectors) The magnitude of F is given by F = L i B sin (θ) where θ is the angle between the direction of i and B. The maximum values is obtained for sin (θ) = 1 or θ = *90°*

A particle with a positive charge of 0.006 C is moving perpendicular to a magnetic field of strength 0.3 T. The particle has a speed of 400 m / s . Calculate the magnitude of the magnetic force exerted on the particle.

The force on a particle of charge q moving at speed v perpendicular to a magnetic field of strength B is given by F = q v B F = (0.006 C) (400 m / s) (0.3 T) *F = 0.72 N*

A straight segment of wire has a length of 30 cm and carries a current of 4.0 A. It is oriented at right angles to a magnetic field of 0.3 T. What is the magnitude of the magnetic force on this segment of the wire?

The force on a wire segment of length L carrying current I and located perpendicular to magnetic field of strength B is F = I L B F = (4.0 A) (0.30 m) (0.3 T) *F = 0.36 N*

A coil of wire of one turn has a cross-sectional area of 0.08 m2. A magnetic field of 0.4 T passes through the coil parallel to the plane of the coil. What is the total magnetic flux through the coil?

The loop is aligned with its area parallel to the magnetic field strength, so the flux through the area is *zero.*

A particle with a positive charge of 0.006 C is moving parallel to a magnetic field of strength 0.3 T. The particle has a speed of 400 m / s . Calculate the magnitude of the magnetic force exerted on the particle.

The velocity of the particle is parallel to the direction of the magnetic field, so there is *no magnetic force on the particle from this field.*

A long, straight, vertical segment of wire traverses a magnetic field of magnitude 2.0 T in the direction shown in the diagram. The length of the wire that lies in the magnetic field is 0.060 m. When the switch is closed, a current of 4.0 A flows through the wire from point P to point Q. [hockey rink w/S zamboni inside and N zamboni outside] Which one of the following statements concerning the effect of the magnetic force on the wire is true?

The wire will be pushed downward, into the plane of the paper.

A wire, connected to a battery and switch, passes through the center of a long current-carrying solenoid as shown in the drawing. When the switch is closed and there is a current in the wire, what happens to the portion of the wire that runs inside of the solenoid?

There is no effect on the wire.

A step-up transformer is used to convert 2000 Volts a.c. to 10,000 Volts a.c. If the primary coil has 100 turns, how many turns must the secondary coil have?

Using the same method as in the previous problem we obtain N2 = (V2 / V1) N1 N2 = (10,000 V / 2000 V) (100 turns) *N2 = 500 turns*

Complete the following statement: The magnetic field around a current-carrying, circular loop is most like that of

a short bar magnet.

21.5 The Force on a Current in a Magnetic Field Example 5 The Force and Acceleration in a Loudspeaker The voice coil of a speaker has a diameter of 0.0025 m, contains 55 turns of wire, and is placed in a 0.10-T magnetic field. The current in the voice coil is 2.0 A. (a) Determine the magnetic force that acts on the coil and the cone. (b) The voice coil and cone have a combined mass of 0.0200 kg. Find their acceleration.

a) *F=ILBsinθ=* *(2.0 A) (55π⋅0.0025 m)(0.10 T)(sin90°)= .86 N* b) *a=F/m= .86 N/ .0200 kg= 43 m/s^2*

Which one of the following materials is not ferromagnetic?

aluminum

A long, straight wire is carrying a current of 5.0 A in the direction shown in the figure. The point P is 0.040 m from the wire. What is the direction of the magnetic field at point P due to the current in the wire?

out of the plane of the page

A negatively charged particle q enters from the left an area with both an electric field directed downward and a magnetic field of magnitude 6.0e-6 T directed into the page (see figure below). What must be the magnitude of the electric field so that the particle is not deflected if the magnitude of its velocity is 2.0×105 cm/s?

q E = q v B E = v B = 2.0×,105 cm/s × 6.0e-6 T = 2.0×,102 m/s × 6.0e-6 T = 1.2 × 10-2 v/m

Complete the following sentence: When a positively-charged particle is released from rest in a region that has a magnetic field directed due east, the particle will

remain at rest.

A proton traveling due west in a region that contains only a magnetic field experiences a vertically upward force (away from the surface of the earth). What is the direction of the magnetic field?

south

A current-carrying, rectangular coil of wire is placed in a magnetic field. The magnitude of the torque on the coil is not dependent upon which one of the following quantities?

the direction of the current in the loop

Complete the following statement: The magnitude of the magnetic force that acts on a charged particle in a magnetic field is independent of

the sign of the charge.