Electric potential is defined as the capacity of a charge to do work. When something is charged, it means that either electrons are supplied to it or they are removed from it. In both these cases, some amount of work is done. This work is stored in the charged object in the form of electric potential. 

The unit of this electric charge is coulomb(C). And, the unit of work done is measured in joules. The unit of electric potential is joules/coulomb. This is also represented by volt. A body has an electrical potential equal to 1 volt if the 1-coulomb charged object does one 1 joule of work.

Electric Potential Energy Formula 

U = qV joules

Potential energy(U) = Charge(q) x Electric Potential (V)

The formula for electric potential energy is basically the product of the charge of a particle and its electric potential.

Electric potential difference can be defined as the amount of work done by a charged object in carrying a unit charge from one point to another within an electric field. In other words, the difference between the point at which there is high potential in the charged body and the point with the low potential in the charged body within the electric field is the potential difference of the body. The unit of this electric potential difference is volt. It is measured using a voltmeter, and it is a scalar quantity.

Consider a unit charge which has different electric potentials (VA and VB). In this case, the potential difference is the difference between the two values of the potential energy of the charged object with unit charge. In other words, potential difference is the difference between the work done by two charged objects each of unit charge. The electric potential derivation is as follows:

ΔV=VB-VA,

Where VA and VB are the electric potentials of the charged object with a unit charge at points A and B of the electric field, respectively. 

This can also be represented as:

ΔV=ΔU/q0 joules/coulomb

ΔV=VA-VB=(UA/q0)-(UB/q0) joules/coulomb,

Where ΔU is the change in potential energy or the work done by the unit charge q0 in an electric field. 

1volt=1joule/1coulomb

This means that a potential difference of 1 volt exists between two points A and B in a constant electric field, if the work done in moving a unit charge from one point to another is equal to 1 joule. 

However, to understand the concept of electric potential at a point in an electric field, we must have a reference to which we assume zero electric potential. This reference point is usually taken at infinity.

The electric potential of a point charge within a uniform electric field is the work done by that point charge with a unit positive charge in moving along any path in the electric field. 

We can assume that the unit positive charge is set at a point. Then, the electric potential (V) at a distance ‘r’ from the charge ‘+q’ is given by the following formula: V=1*q/4πε0*r volt

If the work done in moving this point charge of 1 coulomb from infinity to a specific point in an electric field is 1 joule, the electric potential is equal to 1 volt.

Difference between Electric Potential and Potential Difference

• The electric potential at any point within an electric field is equal to the amount of work done in bringing a unit positive charge from infinity to that point. 
• Potential difference is the work done in carrying a unit positive charge from one point to another point within the electric field while keeping the charge in equilibrium.

1. What is electric potential and potential difference Class 10?

Electric potential is defined as the capacity of a charge to do work. Electric potential difference can be defined as the amount of work done by a charged object in carrying a unit charge from one point to another within an electric field. 

2. What is electric potential?

Electric potential is the capacity of a charged object to do work. When an object is charged, electrons are supplied or removed from it. In both these cases, some amount of work is done.

3. What is the potential difference?

Electric potential difference can be defined as the amount of work done by a charged object in carrying a unit positive charge from one point to another within an electric field. 

4. How is potential difference calculated?

Potential difference can be calculated by measuring the potential energy of an object carrying a unit positive charge between two points within a constant electric field. 

V=U/q, 

Where V is the potential difference, U is the potential energy or work done by the unit charge, and q is the unit charge.

5. Why is potential difference important?

Potential difference, in a way, determines the amount of current that will flow through a system if there is no resistance. It is important because it represents the difference between the potential energies of two bodies carrying a unit positive charge.