A2L Item 245

Goal: Reason and link electrical quantities.

Source: 283-Del C, E, U, etc – cstQ

Two parallel conducting plates form a capacitor. It is isolated and a
charge Q is placed on it. A metal cylinder of length half the plate
separation is then inserted between the plates. Which of the quantities
C, ΔV, Q, E, and U change?

  1. C, E, and U only
  2. ΔV and U only
  3. C and U only
  4. E and U only
  5. C, ΔV, and U only
  6. ΔV and E only
  7. C and ΔV only
  8. None of the above



(8) Students who are formula bound find this a difficult question.
Obviously Q does not change. Depending on how students interpret the
question, they may conclude that E does or does not change. The value of
E in regions outside the cylinder does not change [Students taking this
interpretation may respond #5.], but inside the cylinder it is now zero.
Since E is now zero for half of the distance between the original
plates, both ΔV and U must change. That C also changes can be
appreciated in many different ways.

There are many good follow up questions, such as: Does it make a
difference where the cylinder is placed? How would the quantities change
if the cylinder was made of a dielectric material? Suppose a half
cylinder of length 2d were placed between the plates. How would
quantities change?