Test 2

A solenoid 25.0 cm long and with a cross-sectional area of 0.500 cm2 contains 400 turns of wire and carries a current of 80.0 A. Calculate: a. The magnetic field in the solenoid; b. The energy density in the magnetic field if the solenoid is field with air; c. The total energy contained in the coil's magnetic field d. The inductance of the solenoid.

(a) 0.161 T; (b) 10300 J/m3; (c) 0.129 J; (d) 0.0000402 H

An alpha particle is moving at a speed of 5.0 × 105 m/s in a direction perpendicular to a uniform magnetic field of strength 0.040 T. The charge on an alpha particle is 3.2 × 10-19 C and its mass is 6.6 × 10-27 kg. (a) What is the radius of the path of the alpha particle? (b) How long does it take the alpha particle to make one complete revolution around its path?

(a) 0.26 m (b) 3.2 µs

In Fig. 28.17, a rectangular current loop is carrying current I1 = 9.0 A, in the direction is located near a long wire carrying a current Iw. The long wire is parallel to the sides of the rectangle. The rectangle loop has length 0.80 m and its sides are 0.10 m and 0.70 m from the wire. If the net force on the loop is to have magnitude and is to be directed towards the wire, what must be the (a) magnitude and (b) direction (from top to bottom or from bottom to top in the sketch) of the current Iw in the wire?

(a) 0.32 A (b) from bottom to top

In Fig. 30.6, the current in a solenoid is decreasing at a rate of -7.5 A/s. The self-induced emf in the solenoid is found to be 9.8 V. (a) What is the self-inductance of the solenoid? (b) If the current is in the direction from b to a in the sketch, which point, a or b is at higher potential? The solenoid has negligible resistance.

(a) 1.3 H (b) point a

Consider the circuit sketched above. The battery has emf ε = 19 volts and negligible internal resistance. The inductance is and the resistances are and Use Fig. 30.7 to answer the following questions: (a) Initially the switch S is open and no currents flow. Then the switch is closed. What is the current in the resistor R1 just after the switch is closed? (b) After leaving the switch closed for a long time, it is opened again. Just after it is opened, what is the current in R2?

(a) 1.6 A (b) 2.1 A

A conducting bar moves along frictionless conducting rails connected to a 4.00-Ω resistor as shown in the figure. The length of the bar is 1.60 m and a uniform magnetic field of 2.20 T is applied perpendicular to the paper pointing outward, as shown. (a) What is the applied force required to move the bar to the right with a constant speed of 6.00 m/s? (b) At what rate is energy dissipated in the 4.00 Ω resistor?

(a) 18.6 N (b) 112 W

An electron moves with a speed of 8.0 × 106 m/s along the +x-axis. It enters a region where there is a magnetic field of 2.5 T, directed at an angle of 60° to the +x-axis and lying in the xy-plane. (1 eV = 1.60 × 10-19 C, mel = 9.11 × 10-31 kg) Calculate the magnitude of (a) the magnetic force on the electron. (b) the acceleration of the electron.

(a) 2.8 E-12 N (b) 3.0 E18 m/s

An L-R-C circuit has L = 0.450 H, C = 2.50 × 10-5 F, and resistance R. (a) What is the angular frequency of the circuit when R = 0? (b) What value of R have to give a 5.0 % decrease in angular frequency compared to the value calculated in part (a)?

(a) 298 rad/s (b) 83.8 Ohm

Three resistors are connected across an ideal 2.0-V DC battery as shown in the figure. (a) At what rate does the battery supply energy to the resistors? (b) At what rate is heat produced in the 6.0-Ω resistor?

(a) 3.0 W (b) 0.67 W

A 15.0 - Ω resistor and a coil are connected in series with a 6.30 - V and negligible internal resistance and a closed switch. (a) At 2.00 ms after the switch is opened the current has decayed to 0.210 A. Calculate the inductance of the coil. (b) Calculate the time constant of the circuit. (c) How long after the switch is opened will the current reach 1.00% of its original value?

(a) 43.3 H; (b) 2.89 ms; (c) 13.3 s

In Fig. 27.9, a small particle of charge q = -4.0 × 10-6 C and mass has velocity as it enters a region of uniform magnetic field. The particle is observed to travel in the semicircular path shown, with radius Calculate the (a) magnitude and (b) direction of the magnetic field in the region.

(a) B = 0.15 T (b) directed into the paper

A coaxial cable consists of an inner cylindrical conductor of radius R1 = 0.040 m on the axis of an outer hollow cylindrical conductor of inner radius and outer radius The inner conductor carries current in one direction, and the outer conductor carries current in the opposite direction. What is the value of the magnetic field at the following distances from the axis of the cable: (a) at r = 0.060 m (in the gap midway between the two conductors), and (b) at r = 0.150 m (outside the cable)?

(a) B = 7.33 × 10-6 T; (b) B = 8.99 × 10-6 T

A uniform magnetic field of magnitude 0.80 T in the negative z direction is present in a region of space, as shown in the figure. A uniform electric field is also present and is set at 76,000 V/m in the +y direction. An electron is projected with an initial velocity v0 = 9.5 × 104 m/s in the +x direction. The y component of the initial force on the electron is closest to which of the following quantities? (e = 1.60 × 10-19 C)

-2.4 E-14 N

An electron moving in the direction of the +xaxis enters a magnetic field. If the electron experiences a magnetic deflection in the -y direction, the magnetic field in this region points in the direction of the

-z axis

A long wire carrying a current of 200 A is placed in a uniform external magnetic field of 10.0 mT. The wire is perpendicular to this magnetic field. Locate the points at which the resultant magnetic field is zero.

0.004 m

A charged particle of mass 0.0020 kg is subjected to a magnetic field which acts at a right angle to its motion. If the particle moves in a circle of radius at a speed of what is the magnitude of the charge on the particle?

0.0083 C

A wire along the zaxis carries a current of 1.8 A in the positive z direction. Find the force (magnitude and direction) exerted on an 8.3 cm long length of the wire by a uniform magnetic field with magnitude 0.27 T in the -x direction.

0.040 N, in the -y direction

A 15.00 cm long solenoid with radius 2.50 cm is closely wound with 600 turns of wire. The current in the windings is 8.00 A. What is the magnetic field at a point near the center of the solenoid?

0.0402 T

In Fig. 29.27, a flexible square loop 0.100 m on a side is made of wire of resistance A magnetic field with magnitude 3.70 T is directed onto the plane of the loop. A student crushes the wires together forming a loop of zero area in 0.350 s. Find the total amount of charge flowing through the wire.

0.0463 C

A slender rod, 0.240 m long rotates with an angular speed of 8.80 rad/s about an axis through one end and perpendicular to the rod. The plane of rotation of the rod is perpendicular to a uniform magnetic field with magnitude of 0.650 T. What is the induced emf in the rod?

0.165 V

At a certain instant the current flowing through a 5.0-H inductor is 3.0 A. If the energy in the inductor at this instant is increasing at a rate of 3.0 J/s, how fast is the current changing?

0.20 A/s

The mutual inductance between two coils is 10.0 mH. The current in the first coil changes uniformly from 2.70 A to 5.00 A in 0.160 s. If the second coil has a resistance of 0.600 Ω, what is the magnitude of the induced current in the second coil?

0.240 A

A ten-loop coil having an area of 0.23 m2 and a very large resistance is in a 0.047-T uniform magnetic field oriented so that the maximum flux goes through the coil. The coil is then rotated so that the flux through it goes to zero in 0.34 s. What is the magnitude of the average emf induced in the coil during the 0.34 s?

0.32 V

A long straight conductor carries a current of 100 A. At what distance from the axis is the magnetic field caused by the current equal in magnitude to earth's magnetic field which is 0.5 E-4 T

0.4 m

When a 20.0-ohm resistor is connected across the terminals of a 12.0-V battery, the voltage across the terminals of the battery falls by 0.300 V. What is the internal resistance of this battery?

0.51 Ohms

A conducting rod AB of length 0.25 m is moving to the right with a velocity of 3.0 m/s in a constant magnetic field of 0.8 T pointnig into the paper. What external force must be applied to maintain constant velocity? The complete circuit has resistance R = 0.2 Ohm.

0.6 N

Four resistors are connected across an 8-V DC battery as shown in the figure. The current through the 9-Ω resistor is closest to

0.7 Amps

A galvanometer G has an internal resistance rg. A VOLTMETER is constructed by incorporating the galvanometer and an additional resistance Rs. Which one of the figures below is the most appropriate circuit diagram for the voltmeter?

1 (Straight line)

An L-C circuit consists of a capacitor with C = 3.4 × 10-6 F and an inductor with At the capacitor has charge and the current in the inductor is zero. The circuit oscillates at its resonant frequency. What will be this maximum current?

1 E-2

Three particles travel through a region of space where the magnetic field is out of the page, as shown in the figure. The electric charge of each of the three particles is, respectively,

1 is negative, 2 is neutral, 3 is positive.

A toroidal solenoid has a mean radius of 0.210 m, a cross-sectional area of , and 631 turns. What current is required to produce a stored energy of (Note:

1.0 E-2 A

A proton, with mass 1.67 × 10-27 kg and charge +1.6 × 10-19 C, is sent with velocity in the into a region where there is a uniform electric field of magnitude in the y-direction. What is the magnitude and direction of the uniform magnetic field in the region, if the proton is to pass through undeflected? Assume that the magnetic field has no x-component. Neglect gravitational effects.

1.3 E-2 T in the +z direction

A 30 mF capacitor is charged by connecting it to a 12 V battery. The capacitor is then allowed to discharge by short - circuiting its plates with a wire of resistance 20 Ohm. How long does it take the charge on the capacitor to decay to 1/10 of its original value?

1.4 seconds

An uncharged 30.0-µF capacitor is connected in series with a 25.0-Ω resistor, a DC battery, and an open switch. The battery has an internal resistance of 10.0 Ω and its open-circuit terminal voltage is 50.0 V. The leads have no appreciable resistance. At time t = 0, the switch is suddenly closed. (a) What is the maximum current through the 25.0-Ω resistor and when does it occur (immediately after closing the switch or after the switch has been closed for a long time)? (b) What is the maximum charge that the capacitor receives? (c) When the current in the circuit is 0.850 A, how much charge is on the plates of the capacitor?

1.43 A, right after closing the switch (b) 1500 μC (c) 608 μC

In Fig. 29.24, a uniform magnetic field B is confined to a cylindrical volume of radius 0.05 m. B is directed into the plane of the paper and is increasing at a constant rate of Calculate the magnitude and direction of the current induced in a circular wire ring of radius and resistance that encircles the magnetic field region.

1.43 E-3 CCW

A long thin solenoid has 900 turns per meter and radius 2.50 cm. The current in the solenoid is increasing at a uniform rate of 60. 0 A/s. What is the magnitude of the induced electric field at a point near the center of the solenoid 0.500 cm from the axis of the solenoid?

1.7 E-4

Two coaxial circular coils of radius R = 15 cm, each carrying 4.0 A in the same direction, are positioned a distance d = 20 cm apart, as shown in the figure. Calculate the magnitude of the magnetic field halfway between the coils along the line connecting their centers.

1.9 E-5

A coil of 160 turns and area 0.20 m2 is placed with its axis parallel to a magnetic field of initial magnitude 0.40 T. The magnetic field changes uniformly from 0.40 T in the +x direction to 0.40 T in the -x direction in 2.0 s. If the resistance of the coil is 16 Ω, at what rate is power generated in the coil?

10 W

At what rate would the current in a 100-mH inductor have to change to induce an emf of 1000 V in the inductor?

10,000 A/s

How fast (mph) would a 5.00 cm copper bar have to move at right angles to a 0.650 T magnetic field to generate 1.50 V, across its ends? Does this seem like a practical way to generate electricity?

103 mph not practical

In Fig. 26.17, consider the circuit sketched. The two batteries have negligible internal resistance and emf's and The three resistors have resistances and Calculate the potential difference between points a and b.

13.2 V

A resistor with resistance 640 Ω is in a series with a capacitor of capacitance What capacitance must be placed in parallel with the original capacitance to change the capacitive time constant of the combination to three times its original value?

14 E -6

In Fig. 26.16, consider the circuit sketched. The battery has emf and negligible internal resistance. The four resistors have resistances of and Calculate the rate at which heat is being generated in the resistor R4.

14 W

What inductance would be needed to store 1.00 kW.h of energy in a coil carrying 200 - A current?

180 H

What uniform magnetic field applied perpendicular to a beam of electrons moving at 1.30 × 106 m/s is required to make the electron travel in a circular path of radius 0.35 m?

2.1 E-5 T

In Fig. 27.10, the rectangular loop is pivoted about one side (of length 0.060 m), that coincides with the The end (length 0.020 m) of the loop that lies in the makes an angle of with the as shown in the sketch. The loop carries a current of in the direction shown. (In the side of the loop that is along the the current is in the +y direction.) If there is a uniform magnetic field of magnitude in the -x direction, find the magnitude of the torque that the magnetic field exerts on the loop.

2.3 E-1

An electron traveling toward the north with speed 4.0 × 105 m/s enters a region where the Earth's magnetic field has the magnitude 5.0 × 10-5 T and is directed downward at 45° below horizontal. What is the magnitude of the force that the Earth's magnetic field exerts on the electron? (e = 1.60 × 10-19 C)

2.3 E-18 N

A bar 2.25-m long pivots in a vertical plane about one end. The first 0.500 m of this rod is made of nonconducting material, but the outer 1.75 m are made of iron (see Fig. 29.29). The apparatus is within a uniform 1.20-T magnetic field oriented at right angles to the plane in which the bar rotates. At what angular speed would you need to rotate this bar to generate a potential difference of 8.00 V between the ends of the iron segment?

2.77 rad/s

An air-filled toroidalsolenoid has a mean radius of 15.0 cm and a cross-sectional area of 5.00 cm2 . When the current is 12.0 A, the energy stored is 0.390 J. How many turns does the winding have?

2850

How much energy is stored in a room 3.0 m by 4.0 m by 2.4 m due to the earth's magnetic field with a strength of 5.0 × 10-5 T?

29 mJ

A long solenoid 2.13 meters long and 2.75 cm in diameter, carries a current of 7.75 A. It consists of 10 closed packed layers each with 750 turns along the length. What is the magnetic field at its center?

3.43 E-2 T

For the circuit shown in the figure, all quantities are accurate to 3 significant figures. What is the power dissipated in the 2-Ω resistor?

3.56 W

An electric field of 1.5 kV/m and a magnetic field of 0.40 T act on a moving electron and produce no net force. Calculate the minimum speed of the electron.

3.73 E 3

A circular loop of wire of radius 10 cm carries a current of 6.0 A. What is the magnitude of the magnetic field at the center of the loop?

3.8 E-5

A galvanometer has an internal resistance rg. An ammeter is constructed by incorporating the galvanometer and an additional resistance Rs. Which one of the figures below is the most appropriate circuit diagram for the ammeter?

4 (Single largest rectangle)

What is the self-inductance of a solenoid 30.0 cm long having 100 turns of wire and a cross-sectional area of 1.00 × 10-4 m2?

4.19 mewH

A resistor is made out of a long wire having a length L. Each end of the wire is attached to a terminal of a battery providing a constant voltage V0. A current I flows through the wire. If the wire were cut in half, making two wires of length L/2, and both wires were attached to the battery (the end of both wires attached to one terminal, and the other ends attached to the other terminal), what would be the total current flowing through the two wires?

4I

Sixteen wires, each of length "l" and diameter "d" are in parallel. The resultant resistance is "R". What is the diameter of a single wire for the same resistance?

4d

A very long straight wire carries a 12-A current eastward and a second very long straight wire carries a 14-A current westward. The wires are parallel to each other and are 42 cm apart. Calculate the force on a 6.4 m length of one of the wires.

5.1 E-4

An ideal solenoid is 18.5 cm long, has a circular cross-section 2.20 cm in diameter, and contains 545 equally spaced thin windings. This solenoid is connected in a series circuit with a 15.0-Ω resistor, a battery of internal resistance 5.00 Ω and open-circuit terminal voltage of 25.0 V, and an open switch. . What is the maximum amount of energy that the solenoid will store after closing the switch?

5.99 × 10-4 J

In Fig. 28.16, the two long straight wires are separated by a distance of The currents are to the right in the upper wire and to the left in the lower wire. What is the magnitude and direction of the magnetic field at point P, that is a distance below the lower wire?

6.7 E -6 T directed out of the plane of the paper

Two long parallel wires carry currents of 10 A in opposite directions. They are separated by 40 cm. What is the magnitude of the magnetic field in the plane of the wires at a point that is 20 cm from one wire and 60 cm from the other?

6.7 µT

As shown in the figure, a wire and a 10-Ω resistor are used to form a circuit in the shape of a square, 20 cm by 20 cm. A uniform but nonsteady magnetic field is directed into the plane of the circuit. The magnitude of the magnetic field is decreased from 1.50 T to 0.50 T in a time interval of 63 ms. The average induced current and its direction through the resistor, in this time interval, are closest to

63 mA, from b to a

An L-C circuit consists of a capacitor with C = 3.4 × 10-6 F and an inductor with At the capacitor has charge and the current in the inductor is zero. The circuit oscillates at its resonant frequency. How long after t = 0 will the current in the circuit be maximum?

8.2 E-4

A toroidal solenoid has a mean radius of 0.210 m, a cross-sectional area of 2E-3, and 631 turns. What current is required to produce a stored energy of 0.0300 J

8.89 A

A proton is first accelerated from rest through a potential difference V and then enters a uniform 0.750-T magnetic field oriented perpendicular to its path. In this field, the proton follows a circular arc having a radius of curvature of 1.84 cm. What was the potential difference V?

9.120 kV

An electron experiences a magnetic force of 4.6 × 10-15 N when moving at an angle of 600 with respect to a magnetic field of 3.50 × 10-3 T. Find the speed the electron.

9.48 E6 m/s

In the circuit shown in the figure, all the lightbulbs are identical. Which of the following is the correct ranking of the brightness of the bulbs?

A is the brightest, B and C have equal brightness less than A

Which of the following statements about inductors are correct? There may be more than one correct choice.

An inductor always resists any change in the current through it.

The figure shows two long wires carrying equal currents I1 and I2 flowing in opposite directions. Which of the arrows labeled A through D correctly represents the direction of the magnetic field due to the wires at a point located at an equal distance d from each wire?

B

Consider a solenoid of length L, N windings, and radius b (L is much longer than b). A current I is flowing through the wire. If the length of the solenoid became twice as long (2L), and all other quantities remained the same, the magnetic field inside the solenoid would

Become one Half as strong

The figure shows four different sets of insulated wires that cross each other at right angles without actually making electrical contact. The magnitude of the current is the same in all the wires, and the directions of current flow are as indicated. For which (if any) configuration will the magnetic field at the center of the square formed by the wires be equal to zero?

C

A closed, circular loop has a counter-clockwise current flowing through it as viewed by a person on the right, as shown in the figure. If a second closed circular loop with the same radius approaches this loop with constant velocity along a common axis as shown, in what direction will a current flow in the approaching loop as viewed by the person on the right?

Clockwise

In the circuit shown in the figure, four identical resistors labeled A to D are connected to a battery as shown. S1 and S2 are switches. Which of the following actions would result in the GREATEST amount of current through resistor A?

Closing both switches

A coil lies flat on a tabletop in a region where the magnetic field vector points straight up. The magnetic field vanishes suddenly. When viewed from above, what is the direction of the induced current in this coil as the field fades?

Counter Clockwise

An inductance L and a resistance R are connected to a source of emf as shown. Initially switch S1 is closed, switch S2 is open, and current flows through L and R. When S2 is closed, the rate at which this current changes

Decreases with time

n Fig. 26.15, consider the circuit sketched. Note that two currents are shown. Calculate the emf's ε1 and ε3.

E1 = 28 V E2 = 44 V

A large magnetic flux change through a coil must induce a greater emf in the coil than a small flux change.

False

As more resistors are added in parallel across a constant voltage source, the power supplied by the source

Increases

An RC circuit is connected across an ideal DC voltage source through an open switch. The switch is closed at time t = 0 s. Which of the following statements regarding the circuit are correct? (There may be more than one correct choice.)

Once the capacitor is essentially fully charged, there is no appreciable current in the circuit

Two long parallel wires placed side-by-side on a horizontal table carry identical size currents in opposite directions. The wire on your right carries current toward you, and the wire on your left carries current away from you. From your point of view, the magnetic field at the point exactly midway between the two wires

Points Downward

Ions having equal charges but masses of M and 2M are accelerated through the same potential difference and then enter a uniform magnetic field perpendicular to their path. If the heavier ions follow a circular arc of radius R, what is the radius of the arc followed by the lighter?

R/sqrt(2)

Consider a solenoid of length L, N windings, and radius b (L is much longer than b). A current I is flowing through the wire. If the radius of the solenoid were doubled (becoming 2b), and all other quantities remained the same, the magnetic field inside the solenoid would

Remain the same

The figure shows three identical lightbulbs connected to a battery having a constant voltage across its terminals. What happens to the brightness of lightbulb 1 when the switch S is closed?

The brightness increases permanently

Two light bulbs, B1 and B2, are connected to a battery having appreciable internal resistance as shown in the figure. What happens to the brightness of bulb B1 when we close the switch S?

The brightness of B1 decreases permanently

Two very long parallel wires are a distance d apart and carry equal currents in opposite directions. The locations where the net magnetic field due to these currents is equal to zero are

The net field is not zero anywhere

A circular metal ring is situated above a long straight wire, as shown in the figure. The straight wire has a current flowing to the right, and the current is increasing in time at a constant rate. Which statement is true?

There is an induced current in the metal ring, flowing in a clockwise direction

A horizontal wire carries a current straight toward you. From your point of view, the magnetic field at a point directly below the wire points

To the Right

A vertical wire carries a current straight down. To the east of this wire, the magnetic field points

Toward the South

A vertical wire carries a current upward in a region where the magnetic field vector points toward the north. What is the direction of the magnetic force on this current due to the field?

Toward the west

An electron moving toward the west enters a uniform magnetic field. Because of this field the electron curves upward. The direction of the magnetic field is

Towards the north

A negatively charged particle is moving to the right, directly above a wire having a current flowing to the right, as shown in the figure. In which direction is the magnetic force exerted on the particle?

Upward

The figure shows a bar magnet moving vertically upward toward a horizontal coil. The poles of the bar magnets are labeled X and Y. As the bar magnet approaches the coil it induces an electric current in the direction indicated on the figure (counter-clockwise as viewed from above). What are the correct polarities of the magnet?

X is south, Y is north

A charged particle is moving with speed v perpendicular to a uniform magnetic field. A second identical charged particle is moving with speed 2v perpendicular to the same magnetic field. If the frequency of revolution of the first particle is f,the frequency of revolution of the second particle is

f

In the figure, a bar magnet moves away from the solenoid. The induced current through the resistor R is

from a to b

In the figure, two solenoids are approaching each other with speed v as shown. The induced current through the resistor R is

from a to b

A steady current flows through an inductor. If the current is doubled while the inductance remains constant, the amount of energy stored in the inductor

increases by a factor of 4.

The three loops of wire shown in the figure are all subject to the same uniform magnetic field that does not vary with time. Loop 1 oscillates back and forth as the bob in a pendulum, loop 2 rotates about a vertical axis, and loop 3 oscillates up and down at the end of a spring. Which loop, or loops, will have an emf induced in them?

loop 2 only

The long straight wire in the figure carries a current I that is decreasing with time at a constant rate. The circular loops A, B, and C all lie in a plane containing the wire. The induced emf in each of the loops A, B, and C is such that

loop A has a counter-clockwise emf, loop B has no induced emf, and loop C has a clockwise emf.

A charge is accelerated from rest through a potential difference V and then enters a uniform magnetic field oriented perpendicular to its path. The field deflects the particle into a circular arc of radius R. If the accelerating potential is tripled to 3V, what will be the radius of the circular arc?

sqrt(3)R

A current i flows through an inductor L in the direction from point b toward point a. There is zero resistance in the wires of the inductor. If the current is decreasing,

the potential is greater at point a than at point b.