Question

A dielectric-filled parallel-plate capacitor has plate area A = 25.0 cm2 , plate separation d = 7.00 mm and dielectric constant k = 5.00. The capacitor is connected to a battery that creates a constant voltage V = 15.0 V . Throughout the problem, use ϵ0 = 8.85×10−12 C2/N⋅m2 . Part A Find the energy U1 of the dielectric-filled capacitor. Part B The dielectric plate is now slowly pulled out of the capacitor, which remains connected to the battery. Find the energy U2 of the capacitor at the moment when the capacitor is half-filled with the dielectric. Part C The capacitor is now disconnected from the battery, and the dielectric plate is slowly removed the rest of the way out of the capacitor. Find the new energy of the capacitor, U3. Part D In the process of removing the remaining portion of the dielectric from the disconnected capacitor, how much work W is done by the external agent acting on the dielectric?

Answer 1

Capacitance of a parallel plate capacitor with dielectric between the plates is  

Part A)

Energy of capacitor

Part B)

When half of the dielectric is pulled out, The combination is two capacitors connected in parallel on capacitor with dielectric ( area A/2) and another capacitor with air ( area A/2)

For Capacitor filled with air

For Capacitor filled with dielectric  

Energy of the capacitor

Part C)

Capacitor is disconnected from battery ,

so the charge on the capacitor remains the same

Final charge on capacitor ( without dielectric )

Part D)

Work done by external agent