# What causes resistance when moving parallel plate capacitor plates?

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?

• Are you asking about an ideal case (infinitely large plates, with the distance constant at all times), or real plates? Commented Nov 15, 2016 at 19:18
• 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. Commented Nov 15, 2016 at 19:24

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).