# 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.

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.