Question

. Explain energy store in capacitor ? show that energy density is 1/2 E0E^2​

Answer 1

Energy stored in the capacitor is nothing extraordinary but it's just the electric potential energy and is only dependent on the voltage and charge of the capacitor.

The capacitance of a conductor is C, and initially it's not charged and it gains a potential difference V when we connect it to a battery and if a charge Q is also applied at the same time then,

Q = C*V

Since, Total work done is equal to the product of the potential difference(V) and charge(Q). Therefore, Work Done is W = V*q

If battery gives a small amount of charge dQ at a same or constant potential V, then the work done is

dW = Vdq = qCdq (because V=QC)

Now, total work done in giving a charge of Q to the capacitor is given by

W = = (1/2 )/C = 0.5/C

Substituting  

q = C V

in the equation above, we get

U = 1 /2 C$V^{2}$  

The energy stored in a capacitor is given by the equation U = 1 /2 C$V^{2}$

Energy density is known as total energy per unit volume of a capacitor.

Since, for a parallel plate capacitor,

 A × d = Volume between plates of Capacitor between which electric field E = V / d is applied.

Therefore, Energy(U) stored per unit volume(A*D)

U/(A * D) = ε$E^{2}$/2