# What does electrostatic energy stored in a region mean?

Recently my teacher taught me about Energy density(Energy per unit volume) and told us the formula for the same.

This was explained by taking "Energy" as Energy of a parallel plate Capacitor and dividing it by the volume contained within the capacitor.

And after this I was explained to integrate the Energy Density times volume over a region to get the energy contained in that region.

Now I understand that separating two attracting charges requires energy, which is stored as the potential energy of the "capacitor plates".

But when assigned to a non material object, like energy in a "region" I can't understand what it means at all, nor can I form any intuition regarding this.

Now I understand that separating two attracting charges requires energy, which is stored as the potential energy of the "capacitor plates".

The energy is stored in the electric field between the capacitor plates.

But when assigned to a non material object, like energy in a "region" I can't understand what it means at all, nor can I form any intuition regarding this.

It isn't any "region". It is a region where a field exists. For the capacitor, the energy is stored in the electric field of the region. Similarly, in the case of gravity, the energy is stored in the gravitational field of the region.

Could you tell me what "Energy stored in an electric field" is?What is its practical interpretation?

One definition of energy is it is "the capacity for doing work". An electric field (and gravitational field) has the capacity to do work.

Suppose you have an charged air capacitor, i.e., a capacitor having two plates separated by an air gap. Energy is stored in the electric field in the gap. As proof, if you could place an electron somewhere in the gap it would experience a force due to the electric field causing it to accelerate towards the positively charged plate. That electric force has done work on the electron giving it kinetic energy.

Again, suppose we have a capacitor that was charged by a battery and then the battery removed. There remains a voltage across the charged battery and energy stored in the electric field between the plates. If you now connect say a resistor across the capacitor terminals a current will flow causing heat dissipation in the resistor. Where did the energy come from to create the current and heat? From the electric field between the capacitor plates. Eventually the current will stop when the voltage falls to zero and all the energy stored in the electric field of the capacitor has been used. That initial stored energy was

$$E=\frac{CV^2}{2}$$

Where $$V$$ = the initial voltage of the fully charged capacitor and $$C$$ is the capacitance of the capacitor.

Hope this helps.

• Thank you for the answer! Could you tell me what "Energy stored in an electric field" is?What is its practical interpretation? Aug 19, 2020 at 13:20
• Sure, I’ll update my answer in a little while with examples Aug 19, 2020 at 13:57
• @VamsiKrishna See update to my answer. Aug 19, 2020 at 14:57
• Perfect!I got it! Thank you so much for your time! (+1) Aug 19, 2020 at 15:32