A conductor of length l lies along the x axis with current I

A conductor of length l lies along the x axis with current I in the + X cap direction (phi = 0). Find the work done in turning it at a constant angular speed to phi = pi/2, with one end fixed at origin o, if the uniform magnetic field is B = B_0 Z cap.

Solution

Force per unit length:

dF/dL = i L X B

Evaluate the cross-product then set up the integral:

F = i B L sin ½ dL

F = i ½ B L²

Work done

W = Fds

W = F½ = i ½ B L² = ¼ L²B i

GET THE VALUE OF WORK DONE