Question

A circular coil of 30 turns and radius 8.0 cm carrying a current of 6 A is suspended vertically in a uniform horizontal magnetic field of 1.0 T. The field lines make an angle of 30° with the plane of the coil. Calculate the magnitude of the external torque that must be applied to prevent the coil from turning. What would happen if the circular coil is replaced by a planar coil of irregular shape that encloses the same area, keeping other parameters unchanged?

Answer 1

Given: Number of turns of the coil, N = 30

Radius of the coil, r = 8 cm = 0.08 m

Current in the coil, I = 6 A

Magnetic field strength, B = 1.0 T

Formula: Torque on a Current Loop (τ) = NIAB sin θ

The angle between the magnetic field and the plane of the coil is 30◦. However, the formula requires the angle between the magnetic field and the normal to the coil, so:

θ = 90° − 30°

= 60°

For a circular coil, the area A is given by:

A = πr²

= π(0.08)²

= `22/7 xx 0.0064`

= `0.1408/7`

= 0.0201 m²

τ = NIAB sin θ

= NIAB sin 60°

= `30 xx 6 xx 0.0201 xx 1 xx sqrt3/2`

= 180 × 0.0201 × 0.866

= 3.13 N. m

This is the external torque required to hold the coil in position.

Effect of irregular planar coil to the torque τ depends on:

τ = NIAB sin θ

The shape of the coil does not affect the torque, as long as it encloses the same area. If the circular coil is replaced with an irregular planar coil that encloses the same area, the torque will remain unchanged.