We can “see” the potential energy of a stretched spring in the tension of the coils. If a charged capacitor is analogous to a stretched spring, where is the stored energy? It’s in the electric field!

FIGURE 26.28 shows a parallel-plate capacitor in which the plates have area A and are separated by distance d. The potential difference across the capacitor is related to the electric field inside the capacitor by $\text{Δ}{V}_{\text{C}}=Ed$. The capacitance, which we found in Equation 26.18, is $C={ϵ}_{0}A\text{/}d$. Substituting these into Equation 26.25, we find that the energy stored in the capacitor is

FIGURE 26.28 A capacitor’s energy is stored in the electric field.

The quantity Ad is the volume inside the capacitor, the region in which the capacitor’s electric field exists. (Recall that an ideal capacitor has $\vec{E}=\vec{0}$ everywhere except between the plates.) Although we talk about “the energy stored in the capacitor,” Equation 26.26 suggests that, strictly speaking, the energy is stored in the capacitor’s electric field.

Because Ad is the volume in which the energy is stored, we can define an energy density $u_{\text{E}}$ of the electric field:

The energy density has units $\text{J}\text{/}{\text{m}}^3$. We’ve derived Equation 26.27 for a parallel-plate capacitor, but it turns out to be the correct expression for any electric field.

From this perspective, charging a capacitor stores energy in the capacitor’s electric field as the field grows in strength. Later, when the capacitor is discharged, the energy is released as the field collapses.

We first introduced the electric field as a way to visualize how a long-range force operates. But if the field can store energy, the field must be real, not merely a pictorial device. We’ll explore this idea further in Chapter 31, where we’ll find that the energy transported by a light wave—the very real energy of warm sunshine—is the energy of electric and magnetic fields.