A current carrying wire is in the shape of an equilateral triangle of edge lengt

Question

A current carrying wire is in the shape of an equilateral triangle of edge length 4.0 cm. The triangle lies in the z = 0 plane. The wire carries a current of 1.6 A.

(a) What is the magnitude of the torque on the wire if it is in a region with a uniform magnetic field of magnitude 0.34 T that points in the +z direction?

...................N·m

(b) What is the magnitude of the torque on the wire if it is in a region with a uniform magnetic field of magnitude 0.34 T that points in the +x direction?

..................................N·m

Explanation / Answer

Given length a = 4 cm = 0.04 m

Area of an equilateral triangle is

A = (3/4)*a^2

A = (3/4) * (0.04)^2

A = 6.93 * 10^-4 m^2

current I = 1.6 A

The torque on a loop in a magnetic field is given by

T = I * A * B * sin(theta)

theta is the angle between Area vector and the magnetic field

a)

Here magnetic field and area vector are in +z direction so sin(theta) = 0 hence

torque T = 0

b)

Here theta = 90 so   sin(theta) = 1

therefore   T = I * A * B

T = 1.6 * 6.93 * 10^-4 * 0.34

T = 3.77 * 10^-4 N-m

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