# Homework Help: Torque acting on a movable dielectric

1. Oct 11, 2014

### Wavefunction

1. The problem statement, all variables and given/known data
parallel-plate capacitor consists of two fixed metal semicircles of radius $R$ and a
dielectric plate (susceptibility $\varepsilon$). The plate is able to rotate without friction around the
axis centered at the point $O$ (axis $O$ is perpendicular to the picture). Plate's thickness is $h$ and the plate is filling all the space between capacitor plates. Constant potential difference $V$ is applied to the capacitor. Find the torque $\tau$ acting on the movable dielectric
plate when it is tilted by the angle $\alpha$ as shown on the picture.

2. Relevant equations

$\mathbf{\tau}=\mathbf{p}\times\mathbf{E}$

3. The attempt at a solution

I'm not too sure where to begin on this one, but here's what I think is physically going on: Since the dielectric is not completely within the two capacitors, there is a fringe field which is not parallel to the polarization of the dielectric material which is thus creating a torque on the dielectric.

2. Oct 17, 2014

### Greg Bernhardt

Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?

3. Oct 17, 2014

### Wavefunction

It's okay I have actually solved the question: it was suggested to me by my quantum mechanics TA to view this as a capacitor whose capacitance changes when alpha changes. Then you can use the energy stored in the capacitor and differentiate with respect to alpha in order get the torque :) . Thank you for the response though! Cheers