A 3.02 m long wire loop carrying a current of 2.25 A is in the shape of an equilateral triangle. If the loop is placed in a constant magnetic field of magnitude 0.475 T, determine the maximum torque that acts on it.

0.78 Nm

Explanation:

Parameters given:

Length of the loop, L = 3.02 m

Current in the loop, I = 2.25 A

Magnetic field strength, B = 0.475 T

The torque acting on a loop of wire with radius, r, carrying a current, I, in magnetic field, B, is given as:

τ = N * I * A * B

Where N = number of turns = 1

A = area of loop = pi * r²

We do not have the radius of the loop, but we can find it. The length of the loop is the same as the circumference. Hence, we can find the radius and the area of the loop.

L = 2 * pi * r

3.02 = 2 * pi * r

=> r = 0.481 m

The area, A, will be:

A = pi * r² = pi * 0 481² = 0.726 m²

Therefore, the torque acting on the loop of wire is:

τ = 0.726 * 2.25 * 0.475

τ = 0.78 Nm