A closely wound solenoid of 2000 turns and area of cross-section –4 m2, carrying a current of 4.0 A, is suspended through its centre allowing it to turn in a horizontal plane. (a) What is the magnetic moment associated with the solenoid? (b) What is the force and torque on the solenoid if a uniform horizontal magnetic field of –2 T is set up at an angle of 30° with the axis of the solenoid?
The magnetic moment associated with the solenoid is 1.28 A·m² (or 1.28 J T⁻¹).
Force on the solenoid is zero. Torque on the solenoid is ⁻² N·m.
Explanation
This question tests the concept that a solenoid behaves like a bar magnet with a magnetic moment m = NIA, and the torque on a magnetic dipole in a uniform magnetic field is τ = mB sinθ. The force on a magnetic dipole in a uniform field is zero because there is no net force in a uniform field.