A single circular loop of wire of radius 0.45 m carries a constant current of 2.4 A. The loop may be rotated about an axis that passes through the center and lies in the plane of the loop. When the orientation of the normal to the loop with respect to the direction of the magnetic field is 36 degrees, the torque on the coil is 1.5 N. m. What is the magnitude of the uniform magnetic field exerting this torque on the loop

The magnitude of the uniform magnetic field exerting this torque on the loop is 1.67 T

Explanation:

Given;

radius of the wire, r = 0.45 m

current on the loop, I = 2.4 A

angle of inclination, θ = 36⁰

torque on the coil, τ = 1.5 N.m

The torque on the coil is given by;

τ = NIBAsinθ

where;

B is the magnetic field

Area of the loop is given by;

A = πr² = π(0.45)² = 0.636 m

τ = NIBAsinθ

1.5 = (1 x 2.4 x 0.636 x sin36)B

1.5 = 0.8972B

B = 1.5 / 0.8972

B = 1.67 T

Therefore, the magnitude of the uniform magnetic field exerting this torque on the loop is 1.67 T