**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?

- C, E, and U only
- ΔV and U only
- C and U only
- E and U only
- C, ΔV, and U only
- ΔV and E only
- C and ΔV only
- None of the above

## Commentary:

## Answer

(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?