Parallel Plate Capacitor: Electric field strength, flux & magnetic field

[geoffreythelm]

Homework Statement

This is a question on a past paper of a second-year undergraduate physics paper.

A parallel plate capacitor is charged and the voltage increases at a rate of dV/dt. The plate radius is R and the distance between the plates is d.

(a) What is the electric field strength E(V,d) inside a parallel plate capacitor? (4 marks)

(b) Find the electric flux for a circular area of radius r around the central axis (4 marks)

(c) Derive the magnetic field strength B(r, R, d, dV/dt) (9 marks)

The Attempt at a Solution

(a) Isn't this just E = V/d? Surely that's not worth 4 marks, but I can't imagine what else it could be.

(b) Similarly, isn't this phi = 4 pi k q? (or q/epsilon 0 r^2) O_O Or is it phi = E*d, so E*pi*r^2? SURELY not??

(c) Got a bit stuck with this one. As I wasn't sure about phi, especially. Ended up with

E = (μ0*I)/d + μ0*ε0*(q/ε0*r^2*dt)

Not sure how to progress from there, and especially get it in terms of dV/dt.

Any help would be great.

 

[kuruman]

Part (a), that's it.
Part (b), you might have to express E in terms of V and d. You must use the second expression because the first has to do with a point charge which you don't have here.
Part (c) you need to use Ampere's law as modified by Maxwell.

 

[vela]

(a) Isn't this just E = V/d? Surely that's not worth 4 marks, but I can't imagine what else it could be.

Can you justify why this is correct?

(b) Similarly, isn't this phi = 4 pi k q? (or q/epsilon 0 r^2) O_O Or is it phi = E*d, so E*pi*r^2? SURELY not??

Assuming $k=1/4\pi\epsilon_0$, then $\Phi = 4\pi k q = q/\epsilon_0$ is just Gauss's law, right? While it's a correct statement, it's not a response specific to this problem.

Somehow you then turned that into $\Phi=q/\epsilon_0 r^2$. Where did the $r^2$ come from?

$\Phi = Ed$? I have no idea what you're doing here. Based on your answer to (a), you have $V=Ed$, so you're saying $\Phi = V$? That's not dimensionally correct. Or did you mean something completely different by $d$ which magically seemed to turn into $\pi r^2$ in the next step?

It looks like you're just guessing here. You need to be able to derive what the correct expression for the flux is instead of guessing and hoping for the best.