A circular coil (radius = 0.54 m)has 163 turns and is in a uniform magnetic field.If the orientation of the coil is varied through all possible positions,the maximum torque on the coil by magnetic forces is 0.19 N⋅m when the current in the coil is 2.1 mA.What is the magnitude of the magnetic field?

Question

Quizplus · Accepted Answer

The torque on a current loop in a uniform magnetic field is given by the formula:
τ = NIAB sinθ

where N is the number of turns in the coil, I is the current in the coil, A is the area of the coil, B is the magnitude of the magnetic field, and θ is the angle between the plane of the coil and the direction of the magnetic field.

We are given that the coil has 163 turns, a radius of 0.54 m, and the current in the coil is 2.1 mA. The maximum torque on the coil is 0.19 N⋅m.

When the coil is oriented so that its plane is perpendicular to the magnetic field, the torque is at its maximum value (sinθ = 1). We can plug in the known values and solve for B:
0.19 N⋅m = (163)(2.1 × 10^-3 A)(π(0.54 m)^2)B
B = 0.61 Tesla

Therefore, the magnitude of the magnetic field is 0.61 T, which is answer choice C.

A Circular Coil (Radius = 0