A circular loop of wire carrying a current is located with its center at the origin of coordinates and the normal to its plane having spherical angles 0 , 0 There is an applied magnetic field, B x B 0 (1 y ) and B y B 0 (1 x ) (a) Calculate the force acting on the loop without making any approximat...

a From the above equation it is clear that only B term survives since B is linear in x thus ...

A circular loop of wire carrying a current / is located with its center at the origin

Question:

A circular loop of wire carrying a current / is located with its center at the origin of coordinates and the normal to its plane having spherical angles θ₀, ф₀. There is an applied magnetic field, B_x = B₀(1 + β_y) and B_y = B₀(1 + β_x).

(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?