The expression for the torque on a current loop was derived

Question

The expression for the torque on a current loop was derived assuming that the magnetic field was uniform. But what if B^→ is not uniform? The figure shows a square loop of wire that lies in the xy-plane. The loop has corners at (0,0),(0,L),(L,0), and (L,L) and carries a constant current I in the clockwise direction. The magnetic field has no z-component but has both x- and y-components: B^→ =(B₀y/L)i^+(B₀x/L)j^, where B₀ is a positive constant.

Part A

If the loop is free to rotate about the x-axis, find the magnitude of the magnetic torque on the loop.

Part B

If the loop is free to rotate about the x-axis, find the direction of the magnetic torque on the loop.

If the loop is free to rotate about the y-axis, find the direction of the magnetic torque on the loop.

Part C

If the loop is free to rotate about the y-axis, find the magnitude of the magnetic torque on the loop.

Part D

If the loop is free to rotate about the y-axis, find the direction of the magnetic torque on the loop.

If the loop is free to rotate about the x-axis, find the direction of the magnetic torque on the loop.