## By Pavel Panchekha, Jeffrey Prouty

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

## Level I

1. 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?
2. 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 $$R$$?
3. 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.
4. 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

1. 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.
2. 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.
3. AP Physics C 2008 Electricity & Magnetism, question 3, parts A and B.

## Level III

1. 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.