Answer Happy

3. Magnetic dipole loop A square wire loop with side length L and current i, lying in the z-z plane, is placed in a uniform magnetic field of magnitude B pointing in the positive z-direction. (Assume the magnitude of the current in the loop doesn't change throughout this problem.) 3 z B (a) Write an expression for the magnitude and direction of the force on each side of the loop (the sides are labeled from 1 to 4). Around which axis would the loop rotate due to these forces? (b) Write an expression for the magnetic energy of the loop in the magnetic field, in terms of quantities given in the question, and simplify as much as possible. (Hint: treat the loop at a magnetic dipole). (c) Imagine that the loop has rotated 90 degrees around the axis that you indicated in part a) (in the direction that the forces would cause the loop to rotate). What is the magnitude and direction of the force on each side of the loop and the net force on the loop, in this new orientation? (d) What is the magnetic energy of the loop in this new orientation? Is the magnetic energy of the loop now bigger or smaller than when in its initial orientation?