# Electrical Potential and Potential Difference or Voltage

Before discussing the electrical potential we wish to focus on the gravitational potential to relate these two types of potential. When we lift a body above the ground level, we experience a force acting downward. In other words, the body experiences a force toward the ground. This force is the gravitational force. Hence, obviously, we have done some work to lift the body against the gravitational force. The body stores this work as its potential energy. So, when we release the body, it falls down due to this stored potential energy. This potential developed in the lifted body is the gravitational potential.

Similarly, we can think of electricity charged body. It has its electric field surround it. Suppose this body has a positive charge. Now, we try to bring another positively charged body inside the electric field of the first body. In that case, the second body experiences an electrostatic force outward of the electric field of the first body. Therefore, like gravity, here we also need to do some work against that electrostatic force to bring the second body inside the electric field of the first body. As a result, potential energy develops in the second body. But the potential is not this potential energy or the work done. We measure the potential as the work-done on each coulomb of the charge.  So, practically, the potential energy is the product of the potential of the location and the charge of the body.

Alternatively, we can say the work done on the unit positive charge is numerically equal to the electrical potential of the point in the field.

## Theory of Electric Potential

Practically the electric field surrounds a charged body exists up to an extent. But theoretically, the electric field extends up to infinity. So, theoretically, the electrostatic force on any other charged body placed at the infinity from the former charged body is zero. So the electric potential at the infinity is also zero.

### Definition of Electric Potential

So, the electrical potential of a point in an electric field is the work done per coulomb to bring a charge to that point from the infinity.

### Earth Potential

The potential of the earth is zero. So, we consider the earth as the infinity, in the calculation of the electric potential. So, electric potential means the potential with respect to the earth potential.

### Unit of Electric Potential

The unit of the electric potential is volt. We define one-volt potential as such a potential, which is caused due to bringing a one-coulomb charge from infinity with the work done of one joule.

In other words, for bringing a one-coulomb electrical charge from infinity to a certain point, in an electric field, if we need to perform one-joule work then the potential of the point is considered as one-volt potential.

So, the unit volt is joule per coulomb, means work done per coulomb.

## Electric Potential Difference

As the term indicates, the potential difference is the difference of electrical potential of two different positions in an electric field.

Alternatively, we can assume that it is the difference of work needed to be done per unit coulomb to shift a charged body from infinity to two different points in a field. This statement also means the electric potential difference of two points is the work needs to be done per unit coulomb to shift a charge from one point to the other.

## Electric Potential of a Point

For calculating the electrical potential at a point in an electric field let us consider a charge of + Q coulomb. Now as per Coulomb’s law the expression of the force acting on a unit positive charge at a distance x from + Q is,

Now, we bring the unit positive charge to a slightly nearer position of +Q. For that, we shift the unit positive charge with a small distance dx toward +Q. For that, we need to do the work as expressed below,

The minus sign signifies that to bring the unit positive charge towards +Q, we shift it against the direction of the x. This is the work for shifting the unit positive charge for a distance dx. What work do we need to do for shifting the same from infinity to that new position of the unit positive charge? Say the distance of the new position from +Q is d. Then the expression of the work is

Again, this work numerically equals the potential of the point at the distance d from +Q. In the charge, Q is in coulomb, and the distance, d is in meter, the unit of the work is in joule and the unit of potential is in volt.

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