Alexander Fufaev

Formula: Charge in Radial E-field

Potential Energy of a Charge in a Radial Electric Field

Potential energy

Potential energy of a charged particle with charge \(\class{red}{q}\) in an external electric field. The charge \(\class{red}{q}\) is at a distance \(r\) from the source charge \(\class{red}{Q}\) which generates the electric field.

Electric charge

Electric charge of the particle for which the potential energy is calculated. To bring a positive charge from infinity to the point \(P\) to the positive charge \(\class{red}{Q}\), energy must be invested.

Source charge

Electric charge that generates the electric field.


Distance of the small charge \(\class{red}{q}\) from the source charge \(\class{red}{Q}\).

Vacuum Permittivity

The vacuum permittivity is a physical constant that appears in equations involving electromagnetic fields. It has the following experimentally determined value: $$ \varepsilon_0 ~\approx~ 8.854 \, 187 \, 8128 ~\cdot~ 10^{-12} \, \frac{\mathrm{As}}{\mathrm{Vm}} $$