In the presence of an electric field, work has to be done to move a point charge from some point to another. The electric potential is the amount of work done in moving a point charge from one point to another against an electric field. Suppose we consider a positive charge q situated between two plates, 1 and 2, in the presence of an electric field E. As an electric field is present, the force will be exerted on the charge q, which is equivalent to F=qE. To move this charge, work needs to be done against this electric field, and for that, an equal and opposite force is to be applied, i.e., F= -qE. The work that needs to be performed to move this charge from plate 1 to plate 2 through some distance d will be W=Fd=-qEd. The SI unit of electric potential is joules per coulomb (volts).

Electric Potential Energy

Potential energy is defined as the energy possessed by a body by virtue of its height or position. In the case of electrical potential energy, charges exert forces on each other. As a result, potential energy arises due to the collection of charges. Let’s consider a positive charge q present at some point in the space. If another positive charge is brought closer, both of these charges will experience a repulsive force, and potential energy arises because of that force. The potential energy of a charge Q that is brought closer to the previous charge q will be given by

U = k Q q / r

where k is the coulomb’s constant.

And r is the separation between two charges.

Let’s discuss the variation of electric potential with the electric field. If a positive charge is moved against an electric field, the potential energy will increase. In contrast, if a positive charge is moved in the direction of the electric field, then the potential energy would decrease. In the case of a negative charge, the opposite variation takes place. Electric potential is path independent unless and until a charged particle crosses a magnetic field. 

The difference in potential energies between two points gives us the work done in moving a charge from one point to another.

Electric potential due to a point charge

The basic segment of the matter is an electron, a point charge. You must be familiar with the charge distribution due to a metal surface. This spherical charge distribution creates an external field. Point charges create a similar external electric field. We need to discuss the electric potential in detail due to a point charge.

If electrostatic forces/powers are applied at a point in an electric field, the electric potential is characterised as a measure of the amount of work required to move a positive unit charge from infinity. Consider an electric charge at a point. Due to the presence of an electric field, the charge created by then applies power/force. Whenever r is a distance from the positive charge +q, the electric potential will appear as:

  V = q/4πϵ0r

Where,

In a positive charge, r is the position vector

q is the source charge

Volts are the unit of electric potential, 

                               1 Volt = 1 joule coulomb-¹

The electrostatic potential is supposed to be 1 volt at a point at which work is done by moving a charge of 1 coulomb from infinity to a specific point by means of an electric field against the electrostatic field. 

Superposition of Electric Potential

Electric potential is a scalar quantity, and for a system of charged particles, we can simply add up potentials using algebraic laws. Consider a system of charged particles containing q1, q2, q3… at a distance of r1, r2, r3… from a point. Then, the potential at this point will be