A dielectric-filled parallel-plate capacitor has plate area A = 20.0 cm2 , plate separation d= 9.00 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 0 = 8.8510¹² C2/Nm2

U1= 1.1110⁹JJ

U2= 6.6410¹⁰JJ

a) 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.

b) 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?