# Magnetic Force

1.An electron gun fires electrons into a magnetic field directed straight downward. Find the direction of the force exerted by the field on an electron for each of the following directions of the electron’s velocity: (a) horizontal and due north; (b) horizontal and 30° west of north; (c) due north, but at 30° below the horizontal; (d) straight upward.

2.(a) Find the direction of the force on a proton moving through the magnetic fields in Figure 1, as shown. (b) Repeat part (a), assuming the moving particle is an electron.

[pic]

Figure 1

3.Find the direction of the magnetic field acting on the positively charged particle moving in the various situations shown in Figure 2 if the direction of the magnetic force acting on it is as indicated.

[pic] Figure 2

4.The magnetic field of the Earth at a certain location is directed vertically downward and has a magnitude of 50.0 μT. A proton is moving horizontally toward the west in this field with a speed of 6.

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20 × 106 m/s. What are the direction and magnitude of the magnetic force the field exerts on the proton?

Magnetic Force on a Current-Carrying Conductor

5.A current I = 15 A is directed along the positive x-axis and perpendicular to a magnetic field. A magnetic force per unit length of 0.12 N/m acts on the conductor in the negative y-direction. Calculate the magnitude and direction of the magnetic field in the region through which the current passes.

6.In Figure 1, assume that in each case the velocity vector shown is replaced with a wire carrying a current in the direction of the velocity vector.

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For each case, find the direction of the magnetic force acting on the wire.

7.In Figure 2, assume that in each case the velocity vector shown is replaced with a wire carrying a current in the direction of the velocity vector. For each case, find the direction of the magnetic field that will produce the magnetic force shown.

8.A wire carries a current of 10.0 A in a direction that makes an angle of 30.0° with the direction of a magnetic field of strength 0.300 T. Find the magnetic force on a 5.00-m length of the wire.

9.A wire 2.80 m in length carries a current of 5.00 A in a region where a uniform magnetic field has a magnitude of 0.390 T. Calculate the magnitude of the magnetic force on the wire, assuming the angle between the magnetic field and the current is (a) 60.0°, (b) 90.0°, (c) 120°.

Section 19.6Motion of a Charged Particle in a Magnetic Field

10.A proton moving freely in a circular path perpendicular to a constant magnetic field takes 1.00μs to complete one revolution. Determine the magnitude of the magnetic field.

Section 19.8Magnetic Force between Two Parallel Conductors

11.Two parallel wires are 10.0 cm apart, and each carries a current of 10.0 A. (a) If the currents are in the same direction, find the force per unit length exerted on one of the wires by the other. Are the wires attracted to or repelled by each other? (b) Repeat the problem with the currents in opposite directions.

Section 19.9Magnetic Fields of Current Loops and Solenoids

12.What current is required in the windings of a long solenoid that has 1 000 turns uniformly distributed over a length of 0.400 m in order to produce a magnetic field of magnitude 1.00 × 10−4 T at the center of the solenoid?