What Happens to a Partially Inserted Dielectric in a Capacitor?

[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. Homework Equations
$$W=\frac{1}{2}CV^2=\frac{q^2}{2C}$$
$$F=\frac{dW}{dx}\\ \text{(1)}$$
$$C=εε_r \frac{A}{d} $$

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 weird position.[/B]

 

[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.