A parallel-plate capacitor is constructed from two square aluminum plates
PHYSICS · Multi-part · CBSE · Physics · Electrostatic Potential and Capacitance · Electrostatic Potential and Capacitance
Problem
A parallel-plate capacitor is constructed from two square aluminum plates, each of side length 0.14m, separated by an air gap of 1.0mm. The plates are initially uncharged.
After the capacitor is fully assembled, it is connected to an ideal 12 V battery until equilibrium is reached, and the battery is then disconnected. A slab of dielectric material having uniform thickness that exactly fills the gap is carefully inserted between the plates. The dielectric constant of the slab is κ=4.0.
Ignore edge effects throughout the problem and treat the electric field as uniform inside the capacitor.
(a) Calculate the magnitude of the capacitance before the dielectric is inserted.
(b) Determine the magnitude of the charge residing on each plate immediately after the battery is disconnected, but before the dielectric is inserted.
(c) Once the dielectric is fully inserted, determine the new potential difference between the plates and the magnitude of the electric field inside the dielectric.
(d) Compute the electrical energy stored in the capacitor (i) just after the battery is disconnected but before insertion of the dielectric and (ii) after the dielectric is fully inserted. State whether external work had to be done on the system or whether the system did work on its surroundings during insertion, and justify your answer using energy considerations.