# Problem Set 11 (Given 02/05/12)

## Level I

- Two long parallel wires have a current of \(I\) flowing in opposite directions. If these wires are held at a distance \(d\) apart, what is the magnitude and direction of the magnetic force on each of them?
- A point charge \(Q\) with mass \(m\) travels in a constant magnetic field with magnitude \(B_0\) along the $y$-axis. What is the speed of the particle, given that its path is a circle of radius \(R\)?
- Using Ampere's law, I draw a closed Amperian loop around two wires. One of the wires has current \(+I\) and the other has current \(-I\). Explain why the magnetic field is not necessarily zero at a given point on the loop even though the total enclosed current is zero.
- An infinite solenoid is chopped in half, so that one end goes off to infinity but the other stops at the origin. Draw the magnetic field lines for such a solenoid. Are there any points in space where the magnetic field is zero? Explain.

## Level II

- Use the Biot-Savart law to calculate the magnetic field from a wire of finite length \(L\) with current \(I\) at a point a distance \(d\) away from the center of the wire along a line perpendicular to the wire.
- An infinite slab (a plane of finite thickness) centered on the $xy$-plane has a current density \(J\) (in Coulombs per square meter) and thickness \(h\). The current is directed in the $x$-direction. Find the magnetic field everywhere in space.
- AP Physics C 2008 Electricity & Magnetism, question 3, parts A and B.

## Level III

- Recall from lecture that we found the magnetic field from a single ring of current. By integrating over a series of these rings, find the magnetic field from a finite solenoid of length \(L\) and \(n\) turns per meter without using Ampere's law.