Electric Potential Calculator

Electric potential ($V$) measures the work required to bring a unit positive test charge from infinity to a specific point in an electric field without acceleration. For a single point charge, the formula is expressed as V = k × q / r, where q represents the source charge, r is the radial distance from the charge to the point of interest, and k is the Coulomb constant. The Coulomb constant is defined as k = (8.987551788 × 10⁹) / ε_r, taking into account the relative permittivity (ε_r) of the surrounding medium. For systems with multiple charges, the total electric potential at a specific location is determined by applying the superposition principle, summing the individual potentials contributed by each charge in the configuration.

Imagine you need to find the electric potential generated by a point charge of 5 μC (5 × 10^-6 C) in a vacuum at a distance of 2 meters. First, identify the Coulomb constant in a vacuum (ε_r = 1), which is approximately 8.99 × 10⁹ N·m²/C². Applying the formula V = (8.99 × 10⁹ × 5 × 10^-6) / 2, we multiply the numerator to get 44,950. Dividing this result by the distance of 2 meters yields an electric potential of 22,475 volts (or 22.475 kV).

When using this calculator, ensure all input variables are converted into standard SI units—use Coulombs for charge, meters for distance, and relative permittivity values appropriate for your medium (such as 1 for a vacuum or approximately 5.6 for mica). Pay close attention to the mathematical sign of your charges, as negative charges will generate a negative electric potential that directly reduces the net potential in multi-charge setups.