Question

A capacitor is connected to an ideal battery, and the capacitor is allowed to charge completely. The capacitor is then isolated from the battery, and a material with a dielectric constant of 3 is slowly inserted between the plates of the capacitor. Which of the following correctly describes the process of inserting the material?

A) A force is required to push the material into the space between the plates, and the potential energy stored between the plates of the capacitor will remain the same.
B) A force is required to push the material into the space between the plates, and the potential energy stored between the plates of the capacitor will increase by a factor of 3
C) A force is required to push the material into the space between the plates, and the potential energy stored between the plates of the capacitor will increase by a factor of 9
D) The capacitor will pull the material into the space between the plates, and the potential energy stored between the plates of the capacitor will decrease by a factor of 3
E) The capacitor will pull the material into the space between the plates, and the potential energy stored between the plates of the capacitor will decrease by a factor of 9.

Answer 1

D) The capacitor will pull the material into the space between the plates, and the potential energy stored between the plates of the capacitor will decrease by a factor of 3

Explanation:

points to note

A) inserting a material with dielectric constant of 3 between the plates means that the capacitance C will increase by 3.

B) Since the battery is disconnected, the potential difference V between plate will not remain constant.

C) increasing the capacitance reduces the potential difference across the plate, and from C = Q/V it can be seen that the charges on the plate remains constant.

From the proof in the image below, the reduction in the potential energy of the capacitor is due to the energy used by the capacitor to pull the dielectric material into the space.