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.
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.
