• You would be amazed to know that the simple arrangement of “two plates and an insulating material sandwiched between them” has the ability store energy. This property makes the capacitor useful in a number of ways.
• You will also learn how to derive the equation of energy stored in a capacitor.

Let us derive the formula for the energy stored in a capacitor. Consider an initially uncharged capacitor (just two conducting plates with air or vacuum between them). If we move a charge dq1 from one plate to another, one plate will have acquire +dq1 charge, while the net charge on the other plate becomes -dq1. Since initially there is no electric field present between the plates, charge dq1 will move to another plate without any effort (work).

Now if we move another infinitesimally small amount of charge dq2 to other plate, it will be opposed by the electric field already set up due to charge dq1. Hence some work will be required to be done to move charge dq2 to other plate.

The infinitesimally small amount of word dW is given by.

dW = V * dq1.

This work is stored in the form of potential energy of charge. Again if we move another infinitesimally small charge dq3 from the first plate to the second, it will be opposed by the electric field setup by the charges dq1 + dq2. So q3 will require even more effort (work) to be moved to another plate. If we move total Q amount of charge, then the potential energy stored in a capacitor is given by the integral as follows.

But V= q/C. Hence replacing the value of V in the above equation, we get

Thus the energy stored in a capacitor is given by the formula (1/2)CVor (1/2C)Q2.

## Energy stored in a capacitor per unit volume (Energy density)

We now calculate the energy stored in the capacitor per unit volume. Continuing the formula for the energy stored in the capacitor, we get.

Since A.d is the volume of the capacitor, the energy stored per unit volume is given by