Ch. 20 Math Questions
A vertical straight wire carrying an upward 28-A current exerts an attractive force per unit length of 7.8×10−4 N/m on a second parallel wire 9.0 cm away. What current (magnitude and direction) flows in the second wire?
- 13 A - UP
Jumper cables used to start a stalled vehicle often carry a 65-A current. How strong is the magnetic field 4.5 cm from one cable? Compare to the Earth's magnetic field (5.0×10−5 T).
- 2.9×10−4 T - The magnetic field due to the wire is 5.8 times that of the Earth.
A long horizontal wire carries 24.0 A of current due north. What is the net magnetic field 20.0 cm due west of the wire if the Earth's field there points downward, 44∘ below the horizontal, and has magnitude 5.0×10−5 T?
- 3.8e-5 T - 17deg below horizontal
Determine the magnitude and direction of the force between two parallel wires 25 m long and 4.0 cm apart, each carrying 25 A in the same direction.
- 7.8e-2 N - Towards each other
A 550-turn horizontal solenoid is 15 cm long. The current in its coils is 38 A. A straight wire cuts through the center of the solenoid, along a 3.0-cm diameter. This wire carries a 22-A current downward (and is connected by other wires that don't concern us). What is the force on this wire assuming the solenoid's magnetic field points due east?
0.12 N, South
Alpha particles (charge q=+2e, mass m= 6.6×10^−27 kg) move at 1.6×10^6 m/s. What magnetic field strength would be required to bend them into a circular path of radius r= 0.14 m?
0.24 T
The force on a wire carrying 6.45 A is a maximum of 1.28 N when placed between the pole faces of a magnet. If the pole faces are 55.5 cm in diameter, what is the approximate strength of the magnetic field?
0.358 T
A long thin iron-core solenoid has 380 loops of wire per meter, and a 350-mA current flows through the wire. If the permeability of the iron is 3000μ0, what is the total field B inside the solenoid?
0.5 T
A 1.5-MeV (kinetic energy) proton enters a 0.30-T field, in a plane perpendicular to the field. What is the radius of its path?
0.59 m
A single square loop of wire 22.0 cm on a side is placed with its face parallel to the magnetic field as in Fig. 20-34b. When 5.70 A flows in the coil, the torque on it is 0.325 m⋅N. What is the magnetic field strength?
1.18 T
A 30.0-cm-long solenoid 1.25 cm in diameter is to produce a field of 4.65 mT at its center. How much current should the solenoid carry if it has 935 turns of the wire?
1.19 A
A 240-m length of wire stretches between two towers and carries a 120-A current. Determine the magnitude of the force on the wire due to the Earth's magnetic field of 5.0×10^−5 T which makes an angle of 68∘ with the wire.
1.3 N
An electron experiences the greatest force as it travels 2.8×106 m/s in a magnetic field when it is moving northward. The force is vertically upward and of magnitude 6.2×10−13 N. What is the magnitude and direction of the magnetic field?
1.4 T, EAST
A long pair of insulated wires serves to conduct 24.5 A of dc current to and from an instrument. If the wires are of negligible diameter but are 2.8 mm apart What is the magnetic field 10.0 cm from their midpoint, in their plane (Fig. 20-57)?. Compare to the magnetic field of the Earth.
1.4×10−6 T into the page B is 3% of BE
How much current is flowing in a wire 4.80 m long if the maximum force on it is 0.625 N when placed in a uniform 0.0800-T field?
1.63 A
Protons move in a circle of radius 6.10 cm in a 0.566-T magnetic field. What value of electric field could make their paths straight? In what direction must the electric field point?
1.87e6 N/C
A 3.40-g bullet moves with a speed of 155 m/s perpendicular to the Earth's magnetic field of 5.00×10−5 T. If the bullet possesses a net charge of 18.5×10−9 C, by what distance will it be deflected from its path due to the Earth's magnetic field after it has traveled 1.50 km?
1.97e-6 m
A compass needle points 17∘ E of N outdoors. However, when it is placed 12.0 cm to the east of a vertical wire inside a building, it points 32∘ E of N. What is the magnitude and direction of the current in the wire? The Earth's field there is 0.50×10−4 T and is horizontal.
15 A down into the ground
A circular coil 12.0 cm in diameter and containing nine loops lies flat on the ground. The Earth's magnetic field at this location has magnitude 5.50×10−5 T and points into the Earth at an angle of 56.0deg below a line pointing due north. If a 7.20-A clockwise current passes through the coil a.) determine the torque on the coil b.) which edge of the coil rises up: north, east, south, or west?
2.25e-5 Nm
An iron-core solenoid is 38 cm long and 1.8 cm in diameter, and has 780 turns of wire. The magnetic field inside the solenoid is 2.2 T when 48 A flows in the wire. What is the permeability μ at this high field strength?
2.2×10−5 T*m/A
A mass spectrometer is monitoring air pollutants. It is difficult, however, to separate molecules of nearly equal mass such as CO (28.0106 u) and N2 (28.0134 u). How large a radius of curvature must a spectrometer have (Fig. 20-41) if these two molecules are to be separated on the film by 0.50 mm?
2.5m
A 42-cm-long solenoid, 1.8 cm in diameter, is to produce a 0.030-T magnetic field at its center. If the maximum current is 4.5 A, how many turns must the solenoid have?
2200 turns
The magnetic force per meter on a wire is measured to be only 45% of its maximum possible value. What is the angle between the wire and the magnetic field?
27 degrees
If an electric wire is allowed to produce a magnetic field no larger than that of the Earth (0.50×10−4 T) at a distance of 12 cm from the wire, what is the maximum current the wire can carry?
30 A
A 2.6-m length of horizontal wire carries a 4.5-A current toward the south. The dip angle of the Earth's magnetic field makes an angle of 41∘ to the wire. Estimate the magnitude of the magnetic force on the wire due to the Earth's magnetic field of 5.5×10^−5 T.
4.2×10−4 N METHOD - F = ILBsinTheta
Two straight parallel wires are separated by 7.0 cm. There is a 2.0-A current flowing in the first wire. If the magnetic field strength is found to be zero between the two wires at a distance of 2.2 cm from the first wire, what is the magnitude and direction of the current in the second wire?
4.4 A in the same direction
Two long wires are oriented so that they are perpendicular to each other. At their closest, they are 20.0 cm apart (Fig. 20-59). What is the magnitude of the magnetic field at a point midway between them if the top one carries a current of 20.0 A and the bottom one carries 12.0 A?
4.66×10−5 T
A horizontal compass is placed 18 cm due south from a straight vertical wire carrying a 48-A current downward. In what direction does the compass needle point at this location? Assume the horizontal component of the Earth's field at this point is 0.45×10−4 T and the magnetic declination is 0∘
40deg N of W
A proton and an electron have the same kinetic energy upon entering a region of constant magnetic field. What is the ratio of the radii of their circular paths?
42.8
A rectangular loop of wire is placed next to a straight wire, as shown in Fig. 20-55. There is a current of 3.5 A in both wires. Determine the magnitude and direction of the net force on the loop.
5.1e-6 UP
A straight stream of protons passes a given point in space at a rate of 2.5×109 protons/s. What magnetic field do they produce 1.5 m from the beam?
5.3e-17 T
Determine the magnitude and direction of the force on an electron traveling 7.75×10^5 m/s horizontally to the east in a vertically upward magnetic field of strength 0.45 T.
5.6e-14 N (North)
A galvanometer needle deflects full scale for a 53.0-μA current. What current will give full-scale deflection if the magnetic field weakens to 0.760 of its original value?
69.7 μA
An experiment on the Earth's magnetic field is being carried out 1.00 m from an electric cable. What is the maximum allowable current in the cable if the experiment is to be accurate to ±3.0%?
8.3 A
Two long thin parallel wires 13.0 cm apart carry 28-A currents in the same direction. Determine the magnetic field vector at a point 10.0 cm from one wire and 6.0 cm from the other (Fig. 20-58).
9.5×10−5 T, 82deg above the positive x-axis
A thin 12-cm-long solenoid has a total of 460 turns of wire and carries a current of 2.0 A. Calculate the field inside the solenoid near the center.
9.6×10−3 T
You have 1.0 kg of copper and want to make a practical solenoid that produces the greatest possible magnetic field for a given voltage. Should you make your copper wire long and thin, short and fat, or something else? Consider other variables, such as solenoid diameter, length, and so on. Explain your reasoning.
The wire should be short and fat
Determine the magnetic field midway between two long straight wires 2.0 cm apart in terms of the current I in one when the other carries 25 A. Assume these currents are a.) in the same direction, and b.) in opposite directions.
a.) (2.0×10−5)*(i^2−25 A) b.) (2.0×10−5)*(25 A+i^2)
For a particle of mass m and charge q moving in a circular path in a magnetic field B, a.) show that its kinetic energy is proportional to r2, the square of the radius of curvature of its path. b.) show that its angular momentum is L=qBr2, around the center of the circle.
a.) (q^2*B^2*r^2)/(2m) b.) qBr^2
A Hall probe, consisting of a thin rectangular slab of current-carrying material, is calibrated by placing it in a known magnetic field of magnitude 0.10 T. When the field is oriented normal to the slab's rectangular face, a Hall emf of 12 mV is measured across the slab's width. The probe is then placed in a magnetic field of unknown magnitude B, and a Hall emf of 63 mV is measured. Determine B assuming that the angle θ between the unknown field and the plane of the slab's rectangular face is a.) 90 deg b.) 60 deg
a.) 0.53 T b.) 0.61 T
a.) What is the velocity of a beam of electrons that goes undeflected when moving perpendicular to an electric and to a magnetic field? E and B are also perpendicular to each other and have magnitudes 7.7×10^3 V/m and 7.5×10^−3 T, respectively. b.) What is the radius of the electron orbit if the electric field is turned off?
a.) 1.0×10^6 m/s b.) 7.8×10^−4 m
Suppose the electric field between the electric plates in the mass spectrometer of Fig. 20-41 is 2.88×104 V/m and the magnetic fields are B = B' = 0.68 T. The source contains carbon isotopes of mass numbers 12, 13, and 14 from a long-dead piece of a tree. (To estimate masses of the atoms, multiply by 1.67×10−27 kg.) a.) How far apart are the lines formed by the singly charged ions of each type on the photographic film? b.) What if the ions were doubly charged?
a.) 1.3 mm in both cases. b.) 0.65 mm
Suppose a straight 1.00-mm-diameter copper wire could just "float" horizontally in air because of the force due to the Earth's magnetic field B , which is horizontal, perpendicular to the wire, and of magnitude 5.0×10^−5 T. a.) What current would the wire carry? b.) Does the answer seem feasible? Explain briefly.
a.) 1400 A. b.) This is not realistic since thicker house wiring carries a maximum of 15 Amps safely. This wire would overheat and melt.
A power line carries a current of 95 A west along the tops of 8.5-m-high poles. a.)What is the magnitude and direction of the magnetic field produced by this wire at the ground directly below? How does this compare with the Earth's magnetic field of about 1/2G? b.)Where would the wire's magnetic field cancel the Earth's field?
a.) 2.2e-6 T, South Bw is 4% of Be b.) 0.38m below wire
A long copper strip 1.8 cm wide and 1.0 mm thick is placed in a 1.2-T magnetic field as in Fig. 20-21a. When a steady current of 15 A passes through it, the Hall emf is measured to be 1.02μV. Determine a.) the drift velocity of the electrons b.) the density of free (conducting) electrons (number per unit volume) in the copper
a.) 4.7e-5 m/s b.) 1.1e29 electrons/m^3
a.) What is the force per meter of length on a straight wire carrying a 6.40-A current when perpendicular to a 0.90-T uniform magnetic field? b.) What if the angle between the wire and field is 35.0∘?
a.) 5.8 N/m b.) 3.3 N/m
A helium ion (Q = +2e) whose mass is 6.6×10−27 kg is accelerated by a voltage of 3700 V. a.) What is its speed? b.) What will be its radius of curvature if it moves in a plane perpendicular to a uniform 0.340-T field? c.) What is its period of revolution?
a.) 6e5 m/s b.) 3.6 cm c.) 3.8e-7 s
A toroid is a solenoid in the shape of a donut (Fig. 20-60). Use Ampère's law along the circular paths, shown dashed in Fig. 20-60a, to determine that the magnetic field a.) inside the toroid is B=μ0NI/2πR, where N is the total number of turns b.) outside the toroid is B = 0. c.) Is the field inside a toroid uniform like a solenoid's? If not, how does it vary?
a.) B = (μoNI)/2piR b.) B = 0 c.) Since the field is proportional to 1/R, it is not uniform across the width of the torroid. It changes with distance from the center.
a.) Use Ampère's law to show that the magnetic field between the conductors of a coaxial cable (Fig. 20-61) is B=μ0I/2πr if r (distance from center) is greater than the radius of the inner wire and less than the radius of the outer cylindrical braid (= ground). b.) Show that B = 0 outside the coaxial cable.
a.) B= (μoi/2πr) b.) zero
The Hall effect can be used to measure blood flow rate because the blood contains ions that constitute an electric current. a.) Does the sign of the ions influence the emf? Explain b.) Determine the flow velocity in an artery 3.3 mm in diameter if the measured emf across the width of the artery is 0.13 mV and B is 0.070 T. (In actual practice, an alternating magnetic field is used.)
a.) Sign determines the polarity of the EMF b.) 0.6 m/s
The force on a wire is a maximum of 8.50×10^−2 N when placed between the pole faces of a magnet. The current flows horizontally to the right and the magnetic field is vertical. The wire is observed to "jump" toward the observer when the current is turned on. a.) What type of magnetic pole is the top pole face? b.) If the pole faces have a diameter of 10.0 cm, estimate the current in the wire if the field is 0.220 T. c.) If the wire is tipped so that it makes an angle of 10.0∘ with the horizontal, what force will it now feel? [Hint: What length of wire will now be in the field?]
a.) South b.) 3.86 A c.) 8.50e-2 N
An unknown particle moves in a straight line through crossed electric and magnetic fields with E = 1.5 kV/m and B = 0.034 T. If the electric field is turned off, the particle moves in a circular path of radius r = 2.7 cm. What might the particle be?
it could be a deuteron or an alpha particle, or some other nuclide with an even number of nucleons.
One form of mass spectrometer accelerates ions by a voltage V before they enter a magnetic field B. The ions are assumed to start from rest. Show that the mass of an ion is m=qB2R2/2V, where R is the radius of the ions' path in the magnetic field and q is their charge.
m = (r^2*B^2*q)/2V
In a mass spectrometer, germanium atoms have radii of curvature equal to 21.0, 21.6, 21.9, 22.2, and 22.8 cm. The largest radius corresponds to an atomic mass of 76 u. What are the atomic masses of the other isotopes?
m1 = 70 u m2 = 72 u m3 = 73 u m4 = 74 u
A third wire is placed in the plane of the two wires shown in Fig. 20-57 parallel and just to the right. If it carries 25.0 A upward. What force per meter of length does it exert on each of the other two wires? Assume it is 2.8 mm from the nearest wire, center to center.
near: 4.4×10−2 N/m attractive far: 2.2×10−2 N/m repulsive
A proton, a deuteron, and an alpha particle are accelerated by the same potential difference V and then enter a uniform magnetic field B, where they move in circular paths perpendicular to B. Determine the radius of the paths for the deuteron and alpha particle in terms of that for the proton.
radius (deuteron) = sqrt(2rp) radius (alpha) = sqrt(2rp)
An electron is projected vertically upward with a speed of 1.70×10^6 m/s into a uniform magnetic field of 0.640 T that is directed horizontally away from the observer. Describe the electron's path in this field.
the electron would travel clockwise in a 15.1μm semicircle.
If the current to a motor drops by 12%, by what factor does the output torque change?
τf = 0.88τi
