(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The current I=I_{0}exp(-t) is flowing into a capacitor with circular parallel plates of radius a. The electric field is uniform in space and parallel to the plates.

i) Calculate the displacement current I_{D}through a circular loop with radius r>a from the axis of the system

ii) Calculate an expression for the electric field between the capacitor plates.

3. The attempt at a solution

i) As the plates are being charged up by the current I, the displacement current I_{D}is increasing due to a growing electric field between the plates. I therefore reasoned that as the current I is decreasing with time, the displacement current is increasing with time by an equal amount so the answer would be I_{D}=I_{0}exp(t).

Though I don't know if this is correct.

ii) I used Gauss's law in integral form and a cylinder around the positive capacitor plate.

[itex]\int[/itex]E.dS=Q(t)/ε_{0}

I performed the integration using the top surface of a cylinder, RdRd[itex]\phi[/itex][itex]\hat{z}[/itex]

and ended with the equationE(t)=Q(t)/(ε_{0}πa^{2})[itex]\hat{z}[/itex]

where a=R and I=dQ/dt

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Maxwell's Equations and a circular capacitor

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