Why do we say that electric potential energy is stored in the electric field?

Question

I have been learning electrostatics and came across capacitors. I don't really get why do we say energy is stored in electric field rather than in the charges upon which we or the battery does work. I hope you could provide me the intuition. I don't understand the other answers on the same question.

Answer 1

It can be difficult to see why the electric field has to store energy when studying electrostatics alone. Electrodynamics provides the real motivation. As David Griffiths puts in his text Introduction to Electrodynamics,

When a charge undergoes acceleration, a portion of the field “detaches” itself, in a sense, and travels off at the speed of light, carrying with it energy, momentum, and angular momentum. We call this electromagnetic radiation. Its existence invites (if not compels) us to regard the fields as independent dynamical entities in their own right, every bit as “real” as atoms or baseballs.

So electromagnetic radiation (or light) is made from the electric and magnetic fields alone, without charge. Since light carries energy, the fields must store that energy.

Answer 2

Here is a simple argument that I find suggestive ...

The capacitance of an 'ideal' vacuum-spaced parallel plate capacitor (one for which the plate dimensions are much greater than the plate separation, $d$), is $$C=\frac{\epsilon_0A}d$$ The energy $U$ stored in the capacitor is

$$U=\tfrac 12C\ (\Delta V)^2=\tfrac 12\frac{\epsilon_0A}d\ (\Delta V)^2=\tfrac 12\frac{\epsilon_0A}d\ (Ed)^2=\tfrac 12 \epsilon_0Ad\ E^2$$ We see that if we express $U$ in terms of the magnitude, $E$, of the electric field strength in the space between the plates, then $U$ is proportional to the volume, $Ad$, of that space. To me, this suggests energy storage within that space; for a given $E$, the more field-filled space you have, the more energy you are storing.

Answer 3

I don't really get why do we say energy is stored in electric field rather than in the charges upon which we or the battery does work.

It is stored in both. Electrostatic potential energy, just like other forms of potential energy (gravitational, elastic) is a system property. The charges themselves don't store potential energy nor does the field alone store potential energy. It is the system (combination) of positive and negative charges and the electric field that store electrostatic potential energy.

That stored electrostatic potential energy of the capacitor comes from the work done, by say a battery, to move electrons from one plate (making that plate net positively charged) to the other plate (making the other plate net negatively charged) with an electric field between the plates.

Hope this helps.

Answer 4

If you wiggle charges in the right way, they produce electromagnetic waves. These waves can extend for great lengths. For example, the Voyager space probe is a spacecraft that is headed for deep space. It is currently past the outer edge of the solar system at a respectable 11 billion kilometers and it is still transmitting radio waves. These waves carry energy, equal to $\mathcal E(x)=\epsilon_0E^2(x)$. You can easily imagine these waves in isolation, since these waves have little to do any more with the charges that originally created them.

You can see that these waves carry energy by the fact that after this huge amount of travel, they can still cause charges to oscillate in the receiving antenna here on earth.

Answer 5

There are two things to note here:

1. Electrons are free to move wherever they like to be within any electrical conductor. The steady state is that they do not feel the urge to move at all (ignoring thermal movement). When you have a charged metal sphere, there is no energy available within that metal sphere.

2. If you take an electron from a charged metal sphere, it is going to feel a force near the sphere's surface. And when the electron moves along the direction of that force, it is going to gain/loose energy accordingly. And if this accelerating force is strong enough (high enough field strength), it is going to gain enough energy to knock off another electron from an air molecule before it hits that molecule, allowing a cascade of electrons and ions to form that we call a spark or lightning bolt. This accelerating force does not exist within a conductor, it exists within the isolators around it. We call it the electric field. And it is the source of the energy that the electrons gain in a spark.

We basically use wires to remove any potential difference between two points (unless we talk high frequency AC). The energy, however, moves through the electromagnetic field around those wires. That is where charges are accelerated.