A circular loop of wire carrying a current I is located with its center at the origin of coordinates and the normal to its plane having spherical angles θ0, ϕ0. There is an applied magnetic field, Bx=B0(1+βy) and By=B0(1+βx).
(a) Calculate the force acting on the loop without making any approximations. Compare your result with the approximate result (5.69). Comment.
(b) Calculate the torque in lowest order. Can you deduce anything about the higher order contributions? Do they vanish for the circular loop? What about for other shapes?