Force between plates in condensator

[player1_1_1]

Homework Statement

hello, how can i calculate force which work between two plates in condensator? I tried to write this in this way $$\mbox{d}F=\frac{k\mbox{d}q_1\mbox{d}q_2}{d^2+\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}=\frac{k\rho_q^2\mbox{d}x_1\mbox{d}x_2\mbox{d}y_1\mbox{d}y_2}{d^2+\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}$$
$$F=k\rho_q^2\iiiint\limits_\Omega\frac{\mbox{d}x_1\mbox{d}x_2\mbox{d}y_1\mbox{d}y_2}{d^2+\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}$$
$$\Omega:\left\lbrace x_1^2+y_1^2\le R^2,\ x_2^2+y_2^2\le R^2\right\rbrace$$

how can I calculate it easily? or maybe there is other way to calculate this, without integral?

 

[zzzoak]

One way is to calculate force using energy of condensator

$$F=\frac{dE(x)}{dx}$$

where x is distance between plates.

 

[player1_1_1]

what is this function $$E(x)$$?