   Chapter 19, Problem 39P

Chapter
Section
Textbook Problem

A 6.00-turn circular coil of wire is centered on the origin in the xy-plane. The coil has radius r = 0.200 m and carries a counterclockwise current I = 1.60 A (Fig. P19.39). (a) Calculate tile magnitude of the coil’s magnetic moment. (b) Find the magnitude of the magnetic torque on the coil due to a 0.200-T magnetic field that is directed at an angle θ = 60.0°from the positive z-direction and has components only in the xz-plane. Figure P19.39

a)

To determine
The magnitude of the coils magnetic moment.

Explanation

Given info: The coil has 6 turns. The circular coil has its center at origin. The radius of the coil is 0.200m and carries a counterclockwise current of 1.60A .

Explanation:

The area of the circular coil with radius will be,

A=πr2       (1)

• r is the radius of the circular coil

The magnetic moment of a current carrying coil is,

μ=IAN       (2)

• I is the current in the coil
• A is the area enclosed in the coil
• N is the number of turns in the coil

Combine (1) and (2),

μ=I(πr2)N

substitute 6 for N , 0

b)

To determine
The magnitude of the magnetic torque on the coil.

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