Quasi-electrostatic capacitor

1. Oct 13, 2014

NotHeisenburg

1. The problem statement, all variables and given/known data
I am trying to find the electric and magnetic fields between two parallel circular plates, where one plate is grounded and the the other has a voltage that increases linearly with time. I need the E field between plates, and I can ignore fringing fields. The permativity is specified to be $\epsilon_0$.

2. Relevant equations
$V(t)=at$ where $a$ is a constant.
The radius of the plates is given to be $R$

3. The attempt at a solution
$E(\vec{r},t)=\frac{1}{4\pi\epsilon_0}\int\frac{(\vec{r}-\vec{r}')\rho(\vec{r}',t)d^3r'}{|\vec{r}-\vec{r}'|^3}$

$\rho(\vec{r},t)=$???

With the E field I would find the B field using

$\nabla \times B=\mu_0\vec{J}+\frac{1}{c^2}\frac{\partial E}{\partial t}$

Last edited: Oct 13, 2014
2. Oct 14, 2014

Staff: Mentor

It sounds like a simple parallel plate capacitor setup. You can find the plate area easily enough from the given radius. Do you have a value for plate separation?

3. Oct 14, 2014

NotHeisenburg

I would assume that I could just call the plate separation $d$

4. Oct 14, 2014

Staff: Mentor

Sure. And it's well known that, ignoring edge effects, the electric field between the plates of a parallel capacitor is uniform.