# Problem Set 16 (Given 03/25/12)

- 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?
- AP Physics C 2006 Electricity & Magnetism, question 2
- AP Physics C 2009 Electricity & Magnetism, question 2