a)
Power across capacitor is P=VI
P=VdtdQ
By definition of capacitance, Q=CV
Pdt=CQdQ
Energy stored is
U=∫Pdt=2CQ2...........(i)
Electric field inside the capacitor is given by:
E=εoσ=AεoQ
Capacitance C=dεoA
Q=ECd.........(ii)
Substituting (ii) in (i),
U=2CE2C2d2=2E2εoAd
Energy density AdU=21εoE2
(b)
Let charge on the capacitor before connecting be Q.
After connection, each capacitor has a charge Q/2.
Energy stored before connection, U1=2CQ2
Energy stored after connection, U2=22C(Q/2)2=4CQ2
Hence, energy stored in the combination is less than that of the single capacitor.
