Expression for energy stored per unit volume in a charged parallel plate capacitor
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Work done to store charge Q in a parallel plate capacitor,
W=Q^2/2C
This work is stored as electrostatic potential energy U in the capacitor.
U=Q^2/2C
U=(CV)^2/2C [since Q=CV]
U=1/2 CV^2
The potential difference between plates is V = Ed
where E is the electric field and d is the is the distance between the two plates.
C = εoA/d
U = εoAE^2d^2/2d = εoAdE^2/2
Volume between the plates = Ad
Energy per unit volume = U/Ad = ε
ε = εoE^2/2
W=Q^2/2C
This work is stored as electrostatic potential energy U in the capacitor.
U=Q^2/2C
U=(CV)^2/2C [since Q=CV]
U=1/2 CV^2
The potential difference between plates is V = Ed
where E is the electric field and d is the is the distance between the two plates.
C = εoA/d
U = εoAE^2d^2/2d = εoAdE^2/2
Volume between the plates = Ad
Energy per unit volume = U/Ad = ε
ε = εoE^2/2
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