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# Electric field strength

## Electric field strength

The electric field strength $(E)$ is a quantity used to describe the strength of the field around a source charge . It is a scalar quantity.

The electric field strength at a point in an electric field is the magnitude of the force exerted by the field on a unit positive test charge (i.e. one coulomb).

A test charge is a point charge which has an electric field that is so weak that it does not affect the electric field being examined.

The electric field strength $E$ at the location of a charge $q$ is given by: $$E=\frac{F}{q}$$ $F$ is the magnitude of the electric force on the charge.

The electric field strength is the magnitude of the electric field $\vecphy{E}$, which is a vector quantity. It is therefore important to consider the direction of individual electric fields when adding their electric field strengths together.

The unit of electric field strength is newtons per coulomb $(\text{N C}^{-1})$, obtained by dividing the SI unit of force by the SI unit of charge.

## Electric field strength of a point charge

The electric field strength of a point charge is given by: $$E=\frac{Q}{4\pi\epsilon_{0}r^{2}}$$

This relationship can also be obtained from Coulomb's law, $F=Qq/4\pi\epsilon_{0}r^{2}$, through the formula $E=F/q$.

The electric field strength of a point charge, like the force between two point charges, is inversely proportional to the square of the distance $r$ (i.e. $E\propto r^{2}$).

$E=$electric field strength; $Q=$charge of the source; $r=$distance from the charge; $\epsilon_{0}=$permittivity of free space.