How is energy stored in electric and magnetic fields?

In physics, energy is stored within electromagnetic fields by the work required to establish them.123

Electric Fields

Energy in an electric field is stored by separating electric charges, such as in a capacitor. As charges are moved against the repulsive forces of like charges, work is performed to create an electric field between the plates. The energy stored is equivalent to the work required to establish this field. The energy density (energy per unit volume) of an electric field is given by:12
$$\frac{1}{2}{ϵ}_0{E}^2$$
where ${ϵ}_0$ is the permittivity of free space and $E$ is the magnitude of the electric field.12

Magnetic Fields

Energy in a magnetic field is stored by establishing a current in an inductor, such as a coil of wire. While a steady current flows, energy is stored in the magnetic field created by that current, expressed as:3
$$\frac{1}{2}L{i}^2$$
where $L$ is the self-inductance and $i$ is the current. If the current is interrupted, this stored energy is released, often manifesting as heat or radiation. Large-scale storage of energy in magnetic fields is possible using superconducting magnets.3