Two conducting spherical shells of radii \(a\) and \(b\), with \(b > a\),
are concentric and are not in contact with one another. What is
the capacitance of this arrangement, assuming the area in between
the shells is vacuum?
A dielectric of constant \(k\) fills the entire area between the
plates of a parallel plate capacitor. The dielectric is slowly
removed. How much work has been done on the capacitor when the
dielectric is half way out? Completely removed?
An inductor is constructed using a simple solenoid with length \(L\)
and \(n\) turns per unit length. How will the inductance of this
solenoid change in each of the following cases? Increased
radius, addition of a more permeable core, decreased \(L\) with
constant \(n\), increased \(n\) with constant \(L\).
Describe the initial and steady-state (long term) behavior of a
capacitor in a circuit. What are the physical explanations for
each of these? Do the same for an inductor.
A simple \(R L\) circuit contains a $10 V battery, a 5 ohm resistor,
and a \(0.001\,H\) inductor. This circuit has a switch that closes
at \(t=0\). What is the energy stored in the inductor at this
time? What will be the energy stored in the inductor in the
steady state?