   Chapter 19.6, Problem 19.4QQ

Chapter
Section
Textbook Problem

A square and a circular loop with the same area lie in the xy-plane, where there is a uniform magnetic field B → pointing at some angle θ with respect to the positive z-direction. Each loop carries the same current, in the same direction. Which magnetic torque is larger? (a) the torque on the square loop (b) the torque on the circular loop (c) the torques are the same (d) more information is needed

To determine
Whether the torque on the square loop or the torque on the circular loop is larger.

Explanation

Given info: The circular loop and the square loop have the same area, same current in the same direction. They both are inclined by the same

Explanation:

The torque on a loop in presence of a magnetic field is given by,

τ=μBsinθ (1)

• τ is the torque on the loop
• μ is the magnitude of magnetic moment
• B is the magnetic field
• θ is the angle of inclination of the field and the loop

The magnitude of the magnetic moment is given by,

μ=INA (2)

• N is the number
• I is the current
• A is the area of the loop

From (1) and (2),

τ=NI<

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