Chapter 27, Problem 27.75P

CALC Force on a Current Loop in a Nonuniform Magnetic Field. It was shown in Section 27.7 that the net force on a current loop in a uniform magnetic field is zero. But what if $\stackrel{\to }{\text{B}}$ is not uniform? Figure P27.75 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 x-component but has both y- and z-components: $\stackrel{\to }{\text{B}}$ = (B₀z/L)ĵ + (B₀y/L) $\hat{k}$, where B₀ is a positive constant, (a) Sketch the magnetic field lines in the yz-plane. (b) Find the magnitude and direction of the magnetic force exerted on each of the sides of the loop by integrating Eq. (27.20). (c) Find the magnitude and direction of the net magnetic force on the loop.

Figure P27.75