How Do Voltage Changes Affect Fields in a Quasi-Electrostatic Capacitor?

[NotHeisenburg]

Homework Statement

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 $\epsilon_0$.

Homework Equations

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

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

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

 

[gneill]

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?

 

[NotHeisenburg]

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

 

[gneill]

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

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