Question

part a
find the energy u0 stored in the capacitor.
express your answer in terms of a, d, v, and ε0. remember to enter ε0 as epsilon_0.
view available hint(s)
u0 =
submit
part b
the capacitor is now disconnected from the battery, and the plates of the capacitor are then slowly pulled apart until the separation reaches 3d. find the new energy u1 of the capacitor after this process.

Explanation:

Step1: Recall capacitance formula

The capacitance of a parallel - plate capacitor is $C_0=\frac{\epsilon_0A}{d}$.

Step2: Recall energy formula for capacitor

The energy stored in a capacitor is $U = \frac{1}{2}CV^{2}$. Substitute $C_0$ into the energy formula: $U_0=\frac{1}{2}C_0V^{2}=\frac{1}{2}\times\frac{\epsilon_0A}{d}\times V^{2}=\frac{\epsilon_0AV^{2}}{2d}$.

Answer:

$U_0=\frac{\epsilon_0AV^{2}}{2d}$