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The electric field is perpendicular to the direction of the movement, so the vector product is zero, and thus the force should not exist. What causes it?

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  • $\begingroup$ Are you asking about an ideal case (infinitely large plates, with the distance constant at all times), or real plates? $\endgroup$
    – BowlOfRed
    Commented Nov 15, 2016 at 19:18
  • $\begingroup$ Constant distance but finitely large plates. Basically this: i.imgur.com/KM14BXj.png. I want to know what causes F. And preferably how to calculate it. $\endgroup$
    – TTkacki
    Commented Nov 15, 2016 at 19:24

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While the answer of freecharly is of course correct, I feel there is one point missing, which I think inspired the question.

Even though the electric field between the plates is perpendicular to the direction of motion, the electric field at the edges of the plates is not. It is at these edges where the force acts.

This is also the reason why the force does not depend on the surface of the plates but only on the length of the edges.

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The force in the moving parallel plate capacitor with charge $Q$ is caused by the change in potential energy $$E_{pot}=\frac {Q^2}{2C}$$ where the overlap capacitance is $$C=\frac{\epsilon x b}{d}$$ with $\epsilon$ being the absolute permittivity, $x$ the length, $b$ the width, and d the plate distance of the overlap capacitor. Thus, the larger the overlap the lower the potential energy of the capacitor. Therefore the force in the indicated direction is negative $$F=-\frac {∂E_{pot}}{∂x}$$ the moving plate is drawn in the direction of a larger overlap. See also my answer here: Capacitor with a dielectric with only one plate / with one plate moving (definition of $x$ is different).

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  • $\begingroup$ Is the force equal to zero when the plate is not moving in this case? $\endgroup$
    – TTkacki
    Commented Nov 15, 2016 at 21:36
  • $\begingroup$ @TTkacki - No, the force is not zero when the plate is not moving. The force is always (moving or not) given by the last equation in the answer. $\endgroup$
    – freecharly
    Commented Nov 15, 2016 at 21:40

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