Question

A parallel plate capacitor is charged with a battery and then disconnected from the battery, leaving a certain amount of energy stored in the capacitor. The separation between the plates is then increased. What happens to the energy stored in the capacitor? Discuss your answer in terms of energy conservation.

Short answer

Answer: When the separation between the plates of a parallel plate capacitor is increased, the energy stored in the capacitor decreases. This decrease in energy is due to the conversion of stored energy into work done to increase the plate separation, conserving the total energy of the system.

Step-by-step solution

Recall the formula for energy stored in a capacitor

The formula for the energy stored in a capacitor is given by: Energy, E = 0.5 * C * V^2 where: E = energy, C = capacitance, and V = potential difference (voltage across the capacitor)

Determine the formula for capacitance of a parallel plate capacitor

The capacitance of a parallel plate capacitor is given by: C = (ε * A) / d where: ε = permittivity of the dielectric material between the plates, A = area of each plate, and d = separation between the plates

Substitute the formula for capacitance in the energy formula

We can substitute the capacitance formula into the energy formula: E = 0.5 * ((ε * A) / d) * V^2

Analyze the effect of increasing the separation between the plates on energy stored

As the separation between the plates (d) increases, the capacitance (C) decreases. In our energy equation, energy is inversely proportional to separation: E ∝ 1 / d So, if the separation increases, the energy stored in the capacitor will decrease.

Discuss the energy changes in terms of energy conservation

According to the principle of energy conservation, energy can neither be created nor destroyed. So, as the energy of the capacitor decreases, this energy must be transferred to another form. In this case, the energy stored in the capacitor is converted into work done in pulling the plates apart (against the attractive force between the opposite charges on the plates). In conclusion, when the separation between the plates of a parallel plate capacitor is increased, the energy stored in the capacitor decreases. This decrease in energy is due to the conversion of stored energy into work done to increase the plate separation, conserving the total energy of the system.