# Capacitor and dielectric

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1. Jan 1, 2015

### Patrikp

• 1. The problem statement,
Dielectric plate is placed in capacitor to the half(picture) and it can freely move. Capacitor consists of two parallel plates and is isolated. Consider two cases:
a)charges on plates are constant,
b)voltage is constant.
What happens in each case?

2. Relevant equations

$$W=\frac{1}{2}CV^2=\frac{q^2}{2C}$$
$$F=\frac{dW}{dx}\\ \text{(1)}$$
$$C=εεr \frac{A}{d}$$

3. The attempt at a solution
I know that the answer is that the dielectric will be moving inward in both cases and I even have written solution but I don't understand it. I guess that I should find force on dielectric from (2) but before that i need to determine C which I don't know how to do since dielectric is in wierd position.

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Last edited: Jan 1, 2015
2. Jan 1, 2015

### ehild

How does the capacitance depend on the geometry of the capacitor and the dielectric partially between the plates? Write it in terms of x.