   Chapter 19, Problem 37P

Chapter
Section
Textbook Problem

An eight-turn coil encloses an elliptical area having a major axis of 40.0 cm and a minor axis of 30.0 cm (Fig. P19.37). The coil lies in the plane of the page and carries a clockwise current of 6.00 A. If the coil is in a uniform magnetic field of 2.00 × 10−4 T directed toward the left of the page, what is the magnitude of the torque on the coil? Hint: The area of an ellipse is A = πab, where a and b are, respectively, the semimajor and semiminor axes of the ellipse. Figure P19.37

To determine
The magnitude of the torque on the coil.

Explanation

Given info: The number of turns of the coil is 8 . The coil encloses an elliptic area. The major axis of the ellipse is 40.0cm . The minor axis of the ellipse is 30.0cm . The current flows in the plane of the page carrying clockwise current of 6.00A . The uniform magnetic field of magnitude 2.00×104T directed towards left of the page.

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 field is parallel to the plane the angle has to be 90° .

The area of the elliptical loop will be,

A=πab

• a is the semi major axis
• b is the semi minor axis

The major axis of the ellipse is 40.0cm . Hence,

2a=40.0cma=20.0cm

The minor axis of the ellipse is 30.0cm . Hence,

2b=30.0cma=15.0cm

Hence the torque will become,

τ=nBI(πab)sinθ

Substitute 8 for n , 20.0cm for a , 15

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