The electric field strength $E$ is related to the potential difference $\Delta V_e$ by the formula: $$ E = -\frac{\Delta V_e}{\Delta r} $$
This equation shows that the electric field is the rate of change of electric potential with distance.
Tip
The negative sign indicates that the electric field points in the direction of decreasing potential.
Example
If the potential decreases by $100 \, \text{V}$ over a distance of $0.5 \, \text{m}$, the electric field strength is: $$E = -\frac{-100}{0.5} = 200 \, \text{V m}^{-1}$$
The negative sign indicates the field points in the direction of decreasing potential.
Equipotential Surfaces
An equipotential surface joins all the points that are at the same electric potential.
No work is done moving a charge along an equipotential surface, because the potential does not change ($\Delta V_e = 0$).
Equipotential surfaces are always perpendicular to electric field lines.
Field lines point from high to low potential, so they cross the equipotentials at right angles in the direction of steepest decrease.
Note
Around a point charge the equipotentials are concentric spheres.
Between parallel plates they are flat planes parallel to the plates.
Work in an Electric Field
Work is done when a charge moves in an electric field.
The work done $W$ in moving a charge $q$ through a potential difference $\Delta V_e$ is given by $W = q \Delta V_e$.
This work can be expressed in joules (J) or in electronvolts (eV).
One electronvolt is the energy gained by an electron moving through a potential difference of 1 V, where $1 \, \text{eV} = 1.6 \times 10^{-19} \, \text{J}$.
Example
If a charge $q = 3 \, \mu\text{C}$ moves through a potential difference of $200 \, \text{V}$, the work done is:
