New Energy Stored in a Parallel-Plate Capacitor Calculation

How to calculate the new energy stored in a capacitor with changed plate separation distance?

An air filled parallel-plate capacitor is connected to a 12 Volts battery. The battery is disconnected when it is fully charged to 8.5 nC. The separation distance between the plates is initially 9 cm. If the plates are moved to a new distance of 3 cm, what will be the new energy stored in the capacitor?

Calculation of New Energy Stored in the Capacitor:

First, we need to calculate the initial capacitance of the capacitor using the given data:

Initial Voltage (V) = 12 Volts
Charge (Q) = 8.5 nC
Initial separation distance (d1) = 9 cm
New separation distance (d2) = 3 cm

To calculate the initial capacitance (C1) of the capacitor, we use the formula:

C1 = (ε₀ * A) / d1

where ε₀ is the permittivity of free space and A is the area of the plates.

Next, we calculate the initial energy stored (E1) using the formula:

E1 = (1/2) * C1 * V^2

Then, we calculate the new capacitance (C2) using the formula:

C2 = (ε₀ * A) / d2

Finally, we calculate the new energy stored (E2) using the formula:

E2 = (1/2) * C2 * V^2

By substituting the given values into the formulas, we can find the new energy stored in the capacitor which is 13.60 nJ.