Torque on a Current Loop in a Nonuniform Magnetic Field. In Section 27.7 the expression for the torque on a current loop was derived assuming that the magnetic field B was uniform. But what if B is not uniform? Figure shows a square loop of wire that lies in the xy-plane. The loop has comers 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.
(a) Sketch the magnetic field lines in the y-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) If the loop is free to rotate about the x-axis, find the magnitude and direction of the magnetic torque on the loop.
(d) Repeat part (c) for the case in which the long is free to rotate about the y-axis.
(e) Is Eq. (27.26), I = µ x B, an appropriate description of the torque on this loop? Why or why not?