a) Consider a spherical shell of radius R, with uniform surface charge density, centered on the origin. The shell is spining counterclockwise about the z axis with angular velocity . Find the magnetic vector potential A(r), far from the sphere, using the magnetic dipole approximation. Find the magnetic field B within this approximation. b) Using the method of separation of variables, as applied to the scalar magnetic potential QM. find an expression for the exact magnetic field B both inside and outside the spining charged shell of part (a). How does your answer for the field outside compare with that obtained by the magnetic dipole approximation in part (a)?

An unknown particle travelling with a velocity of 3.12 x 105 m/s enters a 54 mT magnetic field and curves in a circular path with a radius of 12 cm. Determine the charge-to-mass ratio, enter that value in the first blank (with three significant figures of accuracy). From the table of particles on your data sheet (showing data for the charge and mass for alpha particle, electron, proton, and neutron), the identity of the unknown particle is most likely.

A magnetic dipole moment of m = (7.50, -8.38, 4.59) Am² is inside a uniform magnetic field of B = (3.34, -6.77, 6.79) T. What is the potential energy of the dipole? (a) What is the angle between the magnetic dipole moment vector and the magnetic field vector? (b) What is the magnitude of the torque acting on the dipole?

Problem 2 Show that in a current-free volume of space, a static magnetic field can never have a local maximum by considering V(B· B) · da, where S is the surface of a small volume V containing a point P in space.