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 Faradayâ€™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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