A parallel plate capacitor has circular plates of 10 cm radius separated by an air gap of 1 mm. It is charged by connecting the plates to a 100 volt battery. Find the change in energy stored in the capacitor when the plates are moved to a distance of 1 cm and the plates are maintained in connection with the battery.
ΔE=12V2(C1−C2) d=1mm
A=π×1×1=1×10−6m2
ΔE=12V2ϵ0A1(1d−1d+10)
ΔE=12V2ϵ0A(10d(d+10))
ΔE=12×1002×8.824×10−12×10−12×π×1011×10−3
ΔE=1.2623×10−6J
ΔE=1.2623μJ