# 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