Foundational Physics

Short Answer: A capacitor stores energy in the electric field created by separated charges on its plates. Charging the capacitor requires work to move additional charge against the increasing voltage. That work becomes energy associated with the electric field, mainly between the plates of an ideal parallel-plate capacitor. When the capacitor discharges, that energy can be transferred back into the circuit.

Why does separating charge require energy?

Imagine two metal plates that initially have no excess charge. A battery moves electrons from one plate to the other, leaving one plate positively charged and the other negatively charged.

As the charges build up, the electric field between the plates becomes stronger. It takes work to move still more charge in the direction needed to increase that separation, because the growing potential difference opposes further charging.

The energy supplied during charging has not disappeared. It is stored in the electric field produced by the separated charges.

Is the energy on the plates or between them?

The charges themselves are on the metal plates, but the energy is associated with the electric field they create. For large, closely spaced parallel plates, most of that field is in the gap between the plates. There is also some field outside the edges, called the fringing field.

This distinction matters: the plates create and maintain the field, while the field is where the energy is stored. A dielectric placed between the plates can also affect the field and the amount of energy stored under particular conditions.

How much energy can a capacitor store?

A capacitor with capacitance C and voltage V stores energy given by

U = ½CV²

The factor of one-half appears because the capacitor voltage starts near zero and increases while charge is being added. Each additional bit of charge requires more work than the previous one.

For example, a capacitor of 100 microfarads charged to 10 volts stores 0.005 joule, or 5 millijoules. The energy is modest, but it can be released into a connected circuit when the capacitor discharges.

What happens when the capacitor discharges?

Connect the charged capacitor through a resistor. Charge redistributes through the external circuit, the voltage between the plates decreases, and the electric field weakens.

As that happens, the stored field energy is transferred to the circuit, usually becoming thermal energy in the resistor. The capacitor is not creating new energy; it is returning energy that was supplied during charging.

The takeaway

Charges are separated on the plates, but energy is stored in the electric field they produce. Charging builds that field; discharging reduces it and transfers energy to the surrounding circuit.

When This Breaks

The picture of energy being mostly between the plates assumes an ideal parallel-plate capacitor with a nearly uniform field and small fringing effects. In other capacitor shapes, the field and stored energy occupy a different region of space.

Real capacitors also have leakage and losses. Not all energy supplied by a battery during charging remains stored in the capacitor: some may become heat in resistive circuit elements. The expression above gives the energy stored in an ideal linear capacitor at a particular voltage, not the total energy drawn from the battery during charging.

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