1. A long, straight wire carries a current of5.00 A. At one
instant, a proton, 4.00 mm from the wire, travels at 1.50 × 103
m/s parallel to the wire and in the same direction as
the current (Fig. 1). (a) Find the magnitude and direction of
the magnetic field created by the wire. (b) Find the magnitude
and direction of the magnetic force the wire's magnetic
field exerts on the proton.
Fig. 1
2. Two wires, each having a weight per unit length of 1.00 × 10-4 N/m, are parallel,
with one directly above the other. Assume that the wires carry currents that are equal
in magnitude and opposite in direction. The wires are 0.10 m apart, and the sum of the
magnetic force and gravitational force on the upper wire is zero. Find the current in
the wires. (Neglect Earth's magnetic field.)
3. A certain solenoid consists of 100 turns of wire and has a length of 10.0 cm. (a)
Find the magnitude of the magnetic field inside the solenoid when it carries a current
of 0.500 A. (b) What is the momentum of a proton orbiting inside the solenoid in
a circle with a radius of 0.020 m? The axis of the solenoid is perpendicular to the
plane of the orbit. (c) Approximately how much wire would be needed to build this
solenoid? Assume the solenoid's radius is 5.00 cm.
4. The two wires shown in
Fig.2 carry currents of 5.00 A in opposite
directions and are separated by 10.0 cm.
Find the direction and magnitude of the
net magnetic field (a) at a point midway
between the wires, (b) at point P1, 10.0 cm
to the right of the wire on the right, and (c) at point P2, 20.0 cm to the left of
Fig. 2
the wire on the left.
5. A wire carries a 7.00-A current along the x-axis,
and another wire carries a 6.00-A current along the
y-axis, as shown in Fig.3. What is the magnetic
field at point P, located at x = 4.00 m, y = 3.00 m?
Fig. 3
6. In Fig. 4, the current in the long, straight wire is I1 = 5.00 A,
and the wire lies in the plane of the rectangular loop, which carries
10.0 A. The dimensions shown are c = 0.100 m, a = 0.150 m, and l =
0.450 m. Find the magnitude and direction of the net force
exerted by the magnetic field due to the straight wire on the loop.
Fig. 4
7. A single-turn square loop of wire 2.00 cm on a side carries
a counterclockwise current of 0.200 A. The loop is inside a solenoid, with the plane of
the loop perpendicular to the magnetic field of the solenoid. The solenoid has 30 turns
per centimeter and carries a counterclockwise current of 15.0 A. Find the force on
each side of the loop and the torque acting on the loop.
8. Two long parallel conductors carry currents I1 = 3.00 A
and I2 = 3.00 A, both directed into the page in Fig. 5.
Determine the magnitude and direction of the resultant
magnetic field at P.
Fig. 5
9. A uniform horizontal wire with a linear mass density of 0.50 g/m carries a
2.0-A current. It is placed in a constant magnetic field with a strength of 4.0 × 10-3 T.
The field is horizontal and perpendicular to the wire. As the wire moves
upward starting from rest, (a) what is its acceleration and (b) how long does it take to
rise 50 cm? Neglect the magnetic field of Earth.
10. Protons having a kinetic energy of 5.00 MeV are moving in the positive
x-direction and enter a magnetic field of 0.050 T in the z-direction, out of the plane of
the page, and extending from x = 0 to x
= 1.00 m as in Fig.6. (a) Calculate the
y-component of the protons' momentum
Fig. 6
as they leave the magnetic field. (b)
Find the angle α between the initial
velocity vector of the proton beam
and the velocity vector after the beam emerges from the field. [Hint: Neglect
relativistic effects and note that 1 eV = 1.60 × 10-19 J.]
11. The circuit in Figure 7 consists of wires at the top
and bottom and identical metal springs in the left
and right sides. The upper portion of the circuit is
fixed. The wire at the bottom has a mass of 10.0 g
and is 5.00 cm long. The springs stretch 0.500 cm
under the weight of the wire and the circuit has a
total resistance of 12 Ω. When a magnetic field is
turned on, directed out of the page, the springs
stretch an additional 0.300 cm. What is the
magnitude of the magnetic field?
Fig. 7
Ans:
1. (a) 2.50 × 10-4 T, into the page. (b) 6.00 × 10-20 N, to the left.
2. 7.07 A
3. (a) 6.28×10-4 T (b) 2.01×10-24 kg．m/s (c) 31.4 m
4. (a) 4 × 10-5 T, into the page (b) 5 × 10-6 T, out of the page (c) 5/3 × 10-6 T, out of the
page.
5. 0.167 μT out of the page
6. 2.7×10-5 N attract each other.
7. 2.26×10-4 N away from the center, zero torque
8. 13.0 μT toward the bottom of the page.
9. (a) 16 m/s2, (b) 0.25 s
10. (a) -8.00 × 10-21 kg．m/s (b) 8.90°
11. 5.88 × 10-1 T