Answer to Question #163270 in Electricity and Magnetism for Afraid

Question

What is relationship between potential and electric field

Answer 1

The relationship between the electric field and the electric potential is given by the formula:

$$E=-\dfrac{\Delta V}{\Delta r}$$

here, $\Delta V$ is the electric potential, $E$ is the electric field vector which points in the direction of the steepest change in the potential with distance $r$.

As we can see from the formula, the magnitude of the electric field is directly proportional to the rate of change of the electric potential in space. The faster the potential changes from point to point, the larger the electrical field along that displacement.