# 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