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## Homework Statement

A parallel plates capacitor has charge Q and the plates are at distance x. they are separated incremental distance dx. what is the force F to separate them.

## Homework Equations

The capacity: ##C=\varepsilon\frac{A}{x}##

The work done to charge a capacitor: ##W=\frac{1}{2}\frac{Q^2}{C}##

## The Attempt at a Solution

The differential of the capacity:

$$dC=-\frac{\varepsilon A}{x^2}dx$$

The differential of the work:

$$dW=-\frac{Q^2}{2C^2}dC=\frac{\varepsilon A Q^2}{2C^2}\frac{1}{x^2}dx$$

$$F\cdot dx=dW=\frac{\varepsilon A Q^2}{2C^2}\frac{1}{x^2}dx$$

$$F=\frac{\varepsilon A Q^2}{2C^2}\frac{1}{x^2}$$

It should be ##F=\frac{Q^2}{2\varepsilon A}##

Is it reasonable that the force depends on the distance x, as in my result?