Two coils have the same number of circular turns and carry the same current. Each rotates in a magnetic field acting perpendicularly to its axis of rotation. Coil 1 has a radius of 4.5 cm and rotates in a 0.21-T field. Coil 2 rotates in a 0.39-T field. Each coil experiences the same maximum torque. What is the radius (in cm) of coil 2

Explanation:

Torque acting on a coil in a magnetic field = MBsinθ where M is magnetic moment , B is magnetic field and θ is inclination of the normal to coil with direction of field.

For maximum torque sinθ = 1

Maximum torque = MB

M = NIA where N is no of turns , I is current and A is area of the coil

Maximum torque = NIAB

As maximum torque is same

N₁I₁A₁B₁ = N₂I₂A₂B₂

N₁ = N₂ , I₁ = I₂

A₁B₁ = A₂B₂

π R₁² B₁ = π R₂² B₂

4.5² x .21 = R₂² x .39

R₂² = 10.9

R₂ = 3.3 cm .