Energy density of Induced Electric Field

Question

For electrostatic fields, we write the energy density using $$u = frac12epsilon_o E^2$$
is this formula also valid for a non-conservative electric field produced by changing magnetic field?
Or, can we say that the energy stored in a non-conservative electric field per unit charge is equal to the rate of change of flux, given by the formula
$$int E.dl = -partialphi/partial t$$
as the line integral of E is equivalent to work done per unit charge?

Ali Seraj · Answer

In general, the energy density of electromagnetic field in vacuum is given by $u=frac12(|E|^2+|B|^2)$ in suitable unites. The energy can interpolate between electric and magnetic fields. This is what happens in an electromagnetic wave.

Answered by Ali Seraj on May 25, 2021

Ján Lalinský · Answer

Yes, the formula $E=frac{1}{2}epsilon_0 E^2$ is valid for electric field energy density in vacuum (or other medium  such as air that interacts only very weakly with electric field) whether the electric field is purely electrostatic or general (including induced electric field or field of EM waves), but it is necessary that point charges or line charges are not present. Charges have to be distributed with finite density per unit volume. Otherwise total electric energy diverges and validity of the formula is dubious.
The other formula gives induced electromotive force for a circuit (EMF), not energy or energy density.

Energy density of Induced Electric Field

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