Question

A flat, 101 turn current‑carrying loop is immersed in a uniform magnetic field. The area of the loop is 5.61×10−4 m2, and the angle between its magnetic dipole moment and the field is 48.9∘. Find the strength of the magnetic field that causes a torque of 2.75×10−5 N⋅m to act on the loop when a current of 0.00339 A flows in it.

Answer 1

0.2 tesla

Step-by-step explanation:

Number of turn, N = 101

Area, A = 5.61 x 10^-4 m^2

angle between the magnetic moment and magnetic field, θ = 48.9°

Torque, τ = 2.75 x 10^-5 Nm

Current, i = 0.00339 A

Let the magnetic field strength is B.

The formula for the torque is given by

`\tau = M * B * Sin\theta`

where, M is the magnetic moment

M = N x i x A = 101 x 0.00339 x 5.61 x 10^-4 = 1.92 x 10^-4 Am^2

By substitute the values

2.75 x 10^-5 = 1.92 x 10^-4 x B x Sin 48.9°

B = 0.189 Tesla

B = 0.2 Tesla