Rutgers Physics 385 Electromagnetism I (Fall15/Gershtein)

Homework 11 - Due Thursday December 3, 2015 in class

1) Suppose the magnetic field in some region has the form , where k is constant. Find the force on a square loop (side a), lying in the yz plane and centered at the origin, if it carries a current I, flowing counterclockwise, when you look down the x axis.

2) A disk carries a uniform density charge of σ and is rotating around its center at angular velocity ω. What is is the surface current density K at a distance r from the center of the disk?

3) A uniformly charged solid sphere has total charge Q and radius R. It is centered at the origin and is spinning at a constant angular velocity ω about z axis. Find the current density J at any point (r,θ,φ) inside the sphere.

4) Find the magnitude and direction of the magnetic field at point P for the steady current configuration shown below

5) Two parallel wires carry a line charge λ and are distance d from each other. They move at a constant speed as shown below.

How great that speed has to be in order for magnetic force to balance the electrostatic repulsion? Obtain the numerical value - is it a sensible speed?

6) A steady current I flows down a long cyllindrical wire of radius R. Find the magnetic field inside and outside the wire, if:
a) the current is uniformly distributed over the outside surface of the wire
b) the current is distributed in such a way that the current density is proportional to the distance from center of the wire