   Chapter 19, Problem 42P

Chapter
Section
Textbook Problem

A rectangular loop has dimensions 0.500 m by 0.300 m. The loop is hinged along the x-axis and lies in the xy-plane (Fig. P19.42). A uniform magnetic field of 1.50 T is directed at an angle of 40.0° with respect to the positive y-axis and lies parallel everywhere to the yz-plane. The loop carries a current of 0.900 A in the direction shown. (Ignore gravitation.) (a) In what direction is magnetic force exerted on wire segment ab? What is the direction of the magnetic torque associated with this force, as computed with respect to the x-axis? (b) What is the direction of the magnetic force exerted on segment cd? What is the direction of the magnetic torque associated with this force, again computed with respect to the x-axis? (c) Can the forces examined in parts (a) and (b) combine to cause the loop to rotate around the x-axis? Can they affect the motion of the loop in any way? Explain. (d) What is the direction (in the yz-plane) of the magnetic force exerted on segment bc? Measuring torques with respect to the x-axis, what is the direction of the torque exerted by the force on segment bc? (e) Looking toward the origin along the positive x-axis. Will the loop rotate clockwise or counterclockwise? (f) Compute the magnitude of the magnetic moment of the loop. (g) What is the angle between the magnetic moment vector and the magnetic field? (h) Compute the torque on the loop using the values found for the magnetic moment and magnetic field. Figure P19.42

a)

To determine

The direction of magnetic force exerted on the wire segment ab .

Explanation

Given info: The dimension of the rectangular loop is 0.500m by 0.300m. The loop lies on the xy-plane and hinged along the x-axis. The magnitude of the magnetic field is 1.50T and is directed 40° with respect to the positive y-axis and lies parallel everywhere to the yz-plane. The current carries by the loop is 0.900A

b)

To determine

The direction of magnetic torque exerted on the wire segment ab computed with respect to the x-axis.

c)

To determine

The direction of magnetic force exerted on the wire segment cd .

(d)

To determine

The direction of magnetic torque exerted on the wire segment cd computed with respect to the x-axis.

e)

To determine

Whether the magnetic forces on segment ab and cd can combine to rotate the loop.

f)

To determine

The direction of magnetic force exerted on the wire segment bc.

g)

To determine

The direction of magnetic torque exerted by the force on the wire segment bc with respect to the x-axis.

h)

To determine

The direction in which the loop will rotate about the x-axis looking towards the origin along the positive x-axis.

i)

To determine

The magnitude of the magnetic moment of the loop.

j)

To determine

The angle between the magnetic moment vector and the magnetic field.

k)

To determine

The torque on the loop.

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