# Energy density in charged parallel plate capacitor

In this post, we will derive the equation of the **Energy density in charged parallel plate capacitor**.

Energy stored in parallel plate capacitor U = (1/2) C V^{2} where, C is the capacitance of the capacitor and V is the potential difference between the two parallel plates of the above said capacitor.

We know, that the capacitance C of the parallel plate capacitor can be expressed as: C = Aε_{0} /d. Here, ε_{0} = permittivity of air, and d = the separation between the plates, A = area of each plate of the capacitor

The Potential difference V can be expressed as: V = Ed, where E = electric field between the plates

So, Energy stored in parallel plate capacitor U = (1/2) C V^{2}

=> U = (1/2) ( Aε_{0} /d) (Ed)^{2} = (1/2) ( Aε_{0}) (E^{2}d) ………….. (1)

Now, the volume of the space between the plates of the parallel plate capacitor: volume = A d ……………….. (2)

Hence, Energy density u = Energy stored in parallel plate capacitor / volume = (1/2) ( Aε_{0}) (E^{2}d) / A d

=> u = (1/2) ε_{0} E^{2}

**Energy density of parallel plate capacitor = (1/2) ε _{0} E^{2}**