# Square Plate Parallel, with angle, Capacitance Problem

Given two parallel plates, length a. One being on the x axis, starting at the origin. The other starting a distance, d up the y axis at an angle theta (parallel to the x axis), for theta being small. I need to find an equation for an approximation of the capacitance.

I know that if the two plates were purely parallel, C = (E0 * A)/d = (E0 * a^2)/d and that the equation I'm looking for should be (E0 * a^2)/d *( something )
And I know that I need to think of this as a chain of small infinite capacitance in parallel along the angled plate. Meaning I need to do an integral.

I however do not even know where to start. I don't want anyone to just give me the something, but I would love some help on where to start with the integral.

I'm thinking it will have to be and integral (not sure on the limits) of the E field dotted with the ds(or distance).

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berkeman
Mentor
Given two parallel plates, length a. One being on the x axis, starting at the origin. The other starting a distance, d up the y axis at an angle theta (parallel to the x axis), for theta being small. I need to find an equation for an approximation of the capacitance.

I know that if the two plates were purely parallel, C = (E0 * A)/d = (E0 * a^2)/d and that the equation I'm looking for should be (E0 * a^2)/d *( something )
And I know that I need to think of this as a chain of small infinite capacitance in parallel along the angled plate. Meaning I need to do an integral.

I however do not even know where to start. I don't want anyone to just give me the something, but I would love some help on where to start with the integral.

I'm thinking it will have to be and integral (not sure on the limits) of the E field dotted with the ds(or distance).