PhysicsTeacher.in

High School Physics + more

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

See also  Comparison between electric field and magnetic field
Scroll to top
error: physicsTeacher.in