Energy Stored in An Electrostatic Field Distribution
The energy density, or energy per unit volume, of the electrostatic field of a continuous charge distribution is:
-
Outline of proof One may take the equation for the electrostatic potential energy of a continuous charge distribution and put it in terms of the electrostatic field.
Since Gauss' law for electrostatic field in differential form states
where
- is the electric field vector
- is the total charge density including dipole charges bound in a material
- is the permittivity of free space,
then,
so, now using the following divergence vector identity
we have
using the divergence theorem and taking the area to be at infinity where
So, the energy density, or energy per unit volume of the electrostatic field is:
Read more about this topic: Electric Potential Energy
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