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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

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  • 1. 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