Find the dimension of capacitor given [phi]E and Id

[a4pat]

Homework Statement

The electric field between two circular plates of a capacitor is changing at a rate of 1.5x10^6 V/m/s (ΦE). If displacement current at this instant is Id=0.80x10^-8A, find the dimensions of the plates.

Homework Equations

Id=ΔQ/Δt=εΔΦE/Δt
Q=CV=(εA/d)(Ed)

Q=εAE <-- need to solve for A but do not have E.

The Attempt at a Solution

Q=εΦE = (8.85x10^-12)(1.5x10^6)
Q=1.33x10^-5

Feel like I must be missing something, I've gone over this problem and relevant formulas for way too long and can't figure out how to determine A (area of the plates) from the information given. Would really appreciate a push in the right direction.
Thanks

 

[gneill]

What happens if you differentiate your formula Q = (εA/d)(Ed) with respect to time?

 

[a4pat]

What happens if you differentiate your formula Q = (εA/d)(Ed) with respect to time?

Could you elaborate?

I don't see how that helps to solve for A or E

 

[gneill]

Could you elaborate?

I don't see how that helps to solve for A or E

differentiate both sides w.r.t. time. (what varies on each side?). Does the result mesh with any other formula you've written?

 

[a4pat]

differentiate both sides w.r.t. time. (what varies on each side?). Does the result mesh with any other formula you've written?

ΔQ/Δt = CV/Δt = εAE/Δt = Id


Thanks for the reply, still not sure how to solve this. Even with respect to time I can't see how the formulas can be setup to find the plate dimensions (A) without having d, or E.

 

[gneill]

ΔQ/Δt = CV/Δt = εAE/Δt = Id


Thanks for the reply, still not sure how to solve this. Even with respect to time I can't see how the formulas can be setup to find the plate dimensions (A) without having d, or E.

So,

ΔQ/Δt = εA ΔE/Δt by your differentiation

and you're given:

ΔQ/Δt = 0.80x10^-8A ; and ΔE/Δt = 1.5x10^6 V/m/s