Question

A closely wound solenoid of 2000 turns and area of cross-section 1.6 × 10^-4 m² , carrying a current of 4.0 A, is suspended through its centre allowing it to turn in a horizontal plane.

1. What is the magnetic moment associated with the solenoid?

2. What is the force and torque on the solenoid if a uniform horizontal magnetic field of 7.5 × 10^-2 is set up at an angle of 30° with the axis of the solenoid?

Answer 1

1. Magnetic dipole moment, M = nIA

= 2000 × 4.0 × 1.6 × 10^-4 = 1.28 JT^-1 

2. Net force = 0

Torque, τ = MB sinθ

= 1.28 × 7.5 × 10^-2 × sin 30°

= 1.28 × 7.5 × 10^-3 × 1/2 = 4.8 × 10^-2 Nm.