The relationship between electric fields and electric potential is crucial in understanding how charges interact in an electric field. Electric potential, denoted by V, represents the work done by or on a charge to move it from one point to another within an electric field. The unit of electric potential is volts (V).

To calculate electric potential from an electric field, consider a positive test charge brought from a reference point (often taken at infinity) to a specific point in the field. The change in potential energy, W, can be obtained by multiplying the charge, q, by the electric potential, V. The formula for calculating electric potential is:

V = W / q

For example, let's say we have an electric field with a magnitude of 200 N/C. If we move a positive charge of 2 C from a reference point to a specific location, the work done is 400 J. Therefore, the electric potential at that location is 200 V (V = 400 J / 2 C).

The inverse of this process is calculating the electric field from electric potential. Electric field strength, E, is defined as the force experienced by a unit positive charge. The formula to calculate electric field strength is:

E = -∆V / ∆d

Using this formula, we can determine the electric field by taking the negative gradient of electric potential with respect to distance. The negative sign indicates that the field points in the direction of decreasing potential.

For instance, if the electric potential changes by 100 V over a distance of 2 m, then the electric field strength is -50 N/C (E = -100 V / 2 m). The negative sign implies that the field points in the opposite direction of increasing electric potential.