Changing the plate spacing of a parallel plate capacitor and electrical energy

Problem Statement

A parallel-plate capacitor with plate area $S$S and plate spacing $d$d is placed in a vacuum. This capacitor is connected to a DC power supply with voltage $V$V, and a sufficient amount of time has elapsed. The permittivity of vacuum is $\varepsilon_0$ε0​.

Next, while the capacitor remains connected to the power supply, an external force is applied to counteract the attractive force between the plates, slowly widening the plate spacing from $d$d to $3d$3d. During this change, the capacitance of the capacitor plates and the stored charge change.

Find the algebraic expression (using $\varepsilon_0$ε0​, S, d, and V$) of the work done by the power supply (electrical energy flowing into the power supply) during the process of widening the plate spacing.

Constraints

• $\varepsilon_0 = 8.85 \times 10^{-12} \text{ F/m}$ε0​=8.85×10−12 F/m
• $S = 0.200 \text{ m}^2$S=0.200 m2
• $d = 2.00 \times 10^{-3} \text{ m}$d=2.00×10−3 m
• $V = 300 \text{ V}$V=300 V

Input Format

When the magnitude of work done by the power supply, $W \text{ [J]}$W [J], is calculated, it becomes $A \times 10^{-7} \text{ J}$A×10−7 J. Find the value of the coefficient $A$A in this case and input a natural number representing that value.