Question

A current-carrying wire is in the shape of a square of edge length 5.0 cm. The square lies in the z = 0 plane. The wire carries a current of 2.1 A.

(a) What is the magnitude of the torque on the wire if there is a uniform magnetic field of magnitude 0.28 T in the +z direction?

(b) What is the magnitude of the torque if the field is in the +x direction?

Answer 1

Area, A = 5.0*5.0 cm^2 = 25.0*10^-4 m^2 (k-direction)

I = 2.1 A (given)

M = IA = 2.1*25.0*10^-4 = 5.25*10^-3 Am^2 (k-direction)

Part A)

B = 0.28 T (k-direction)

Torque, T = M(k-direction) x B(k-direction)

Magnitude of torque on the wire, T = 0

(Since, Vector Product between two vectors in same direction is Zero)

Part B)

B = 0.28 T (x-direction)

Torque, T = M(k-direction) x B(x-direction) = 5.25*10^-3 Am^2 (k-direction) x 0.28 T (x-direction)

Magnitude of Torque, T = 1.47*10^-3 Nm