Problem Set 16 (Given 03/25/12)

  1. 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?
  2. 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?
  3. 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 \(L\).
  4. 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.
  5. 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?
  6. AP Physics C 2006 Electricity & Magnetism, question 2
  7. AP Physics C 2009 Electricity & Magnetism, question 2

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