In a certain region, the magnetic field is specified by B = B₀ (1 + x l ) k . A square loop carrying a current i and having an edge length l is situated with its edges parallel to the x and y axes. Determine the magnitude of the net magnetic force experienced by the loop.

Step-by-step solution

Consider the square loop placed in the xy -plane with its vertices at (x, y) , (x+l, y) , (x+l, y+l) , and (x, y+l) . The magnetic force on a current element is d F = i(d l B ) . For the two edges parallel to the x -axis, the current flows in opposite directions. Since the magnetic field B = B₀ (1 + x l ) k depends only on x , the forces on these two edges are equal in magnitude and opposite in direction, cancelling each other out. For the edge at x + l parallel to the y -axis, the force is: F ₁ = i(l j ) [B₀ (1 +