Question

Derive the energy density of a capacitor.​

Answer 1

Answer:

In order to charge a capacitor certain work is done against the electrostatic force of repulsion, This work done is stored in the form of electric energy of the capacitor. The energy density of a capacitor is the energy stored per unit volume. It is denoted by u.

Explanation:

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Answer 2

• If we multiply the energy density by the volume between the plates, we obtain the amount ofenergy stored between the plates of a parallel-plate capacitor
• UC = uE(Ad) = 12ϵ0E2Ad = 12ϵ0V2d2Ad = 12V2ϵ0Ad = 12V2C.
• In this derivation, we used the fact that the electrical field between the plates is uniform so that E=V/d and C=ϵ0A/d.