A parallel plate capacitor is charged with a time dependent current

Each plate of the capacitor is circular in shape with radius R and the distance between the plates is D as shown in the picture below.

a) Find the Electric Field within the plates.

b) Find the induced magnetic field within the plates due to the displacement current (i.e due to the change in the electric flux).

c) Write down an integral equation to calculate the magnetic flux passing through a rectangular area in between the plates.

d) Using your answer to Part c, find the total magnetic flux and determine the self-inductance of this parallel plate capacitor. Find the resonance frequency above which the capacitor behaves like an inductor (some electronics knowledge may be required).

e) Using your answer to Part c, find the first order correction to the electric field (i.e the change in the magnetic flux also induces an electric field due to Faraday’s Law), and find the net electric field after including this first order correction to the field found in Part a.


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