   Chapter 19, Problem 36P

Chapter
Section
Textbook Problem

A current of 17.0 mA is maintained in a single circular loop with a circumference of 2.00 m. A magnetic field of 0.800 T is directed parallel to the plane of the loop. What is the magnitude of the torque exerted by the magnetic field on the loop?

To determine
The magnitude of the torque exerted by the magnetic field on the loop.

Explanation

Given info: The circumference of the circular loop is 2.00m . A magnetic field of 0.800T is directed parallel to the plane of the loop. The wire loop carries a current of 17.0mA .

Explanation:

The torque applied on a circular loop is given by,

τ=nBIAsinθ

• n is the number of turns in the loop
• B is the magnetic field
• I is the current on the wire
• A is the area enclosed by the loop
• θ is the angle between the line normal to the plane of the loop and the magnetic field

Since the magnetic field direction is parallel to the plane to the loop the angle has to be 90° .

The circumference of the loop is given by,

C=πd

• C is the circumference of the circular loop
• d is the diameter of the circle

So the diameter of the circular loop will be,

d=Cπ

The area of the circular loop will be,

A=πd24=π4(Cπ)2

Hence the torque will become,

τ=nBIπ4(Cπ)2sinθ

Substitute 1 for n , 2

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