High School Physics

# 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 V2 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 = Aε0 /d. Here, ε0 = 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 V2

=> U = (1/2) ( Aε0 /d) (Ed)2 = (1/2) ( Aε0) (E2d) ………….. (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) ( Aε0) (E2d) / A d

=> u = (1/2) ε0 E2

Energy density of parallel plate capacitor = (1/2) ε0 E2

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