# Energy stored in a capacitor equation derivation and problems

## Energy stored in a capacitor equation

Consider a capacitor with the capacitance ‘C’ ,which is connected to the battery of emf ‘V’ .If ‘dq’ charge is transferred from one plate to other,then the work done ‘dW’ will be:
dW =V dq
This work done is stored in the form of electric potential energy ‘dU’
dU =V dq
When the capacitor is fully charged then the total energy stored is:

The energy stored in the capacitor is the energy store in the electric field between its plates.So,the energy stored can be expressed in terms of electric field strength ‘E’.

## Energy density:

The energy density ‘μ’ is described as the energy stored ‘U’ per unit volume ‘V’ .mathematically it is expressed as:

If any dielectric medium having dielectric constant ‘Ke‘ is placed between the plates of a capacitor,then the expression of energy stored in the electric field of capacitor ‘U’ and energy density ‘μ’ will become:

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