The energy required to charge a parallel plate condenser of plate separation d and plate area of cross-section A such that the uniform electric field between the plates is E is :

CONCEPT: ​

• The capacitance of a capacitor (C): The capacity of a capacitor to store the electric charge is called capacitance.
  • The capacitance of a conductor is the ratio of charge (q) to it by a rise in its potential (V).

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• The Capacitance of a Parallel Plate Capacitor with the distance between plates d and area of Cross-Section A is given as

 \(C = \frac{A\varepsilon _{0}}{d}\)--- (1)

ε0 is the Permittivity of free space.

• The energy (U) supplied by a battery to charge a Capacitor of Capacitance C at Potential Difference V is Given as:

U = CV²  ----- (2)

• The potential difference between two points at distance d and Electric Field E is Given as

V = E.d ---- (3)

CALCULATION:

The energy required to Charge a capacitor will be provided by Battery. 

So, Energy Required is Given by Eq (2)

Now, Putting Eq (1) and Eq (3) in Eq (2) We get

 \(U = \frac{A\varepsilon _{0}}{d} \times (Ed)^{2}\)

⇒ U = ε0E2 Ad

Additional Information

• The Energy Stored in a Capacitor is Given as \(\frac{1}{2}CV^{2}\) and Energy Provided by Battery is CV². So, to charge a capacitor twice of energy is to be supplied by the battery.