When a mass is
raised above the ground level, work is done against the force of gravity. This
work done is stored in the mass as a potential energy (mgh). Hence, due to
such, potential energy it is said that the mass, when raised above the ground
level has a gravitational potential such. Potential of mass depends upon the
position of the mass with respect to the ground.

An electric
charge gives rise to an electric field around it, analogous to gravitational
field around the earth. If any charge is introduced in this field, it gets
attracted or repelled, depending on the nature of the charge. At the time of
movement of this charge, work is done against or by the force acting on the
charge due to the electric field. This depends on the position of the charge in
the electric field and is analogous to the proportional of mass due to
gravitation field, when lifted upwards.

Now, consider
a small isolated positive charge 'q' placed at infinity with respect to another
isolated positive charge 'q' as shown in the Fig 1. theoretically, the electric
field of charge 'q' extends upto infinity but has a zero influence at infinity,
where 'q' is placed. When charge 'q' is moved towards 'Q', work is done against
the force of repulsion between these two like charges.

Due to this
work done, when charge 'q' reaches position A, it acquires a potential energy.
If charge 'q' is released, due to force of repulsion, it will go back to
infinity i.e. position of zero potential. So, at point A, charge 'q' has some
potential exactly equal to work done in bringing it from infinity to the point
A, called electric potential.

It can be
defined as the work done in joules, in moving a unit positive charge from
infinity (position of zero potential) to te point against the electric field.

It is denoted
by symbol V and is measured in joule per coulomb or volt.

**Definition of 1 volt :**

The electric
potential at a point in an electric field is said to be one volt when the work
done in bringing a unit positive charge from infinity to that point from
infinity against the electric field is one joule.

__1.1 Potential Difference__

Consider two
points A and B in an electric field as shown in Fig 2. The positive charge '+q'
is moved from point A to B in an electric field. At point A, charge acquires
certain electric potential say V

_{A}. Some additional work is done in bringing it to point B, it has an electric potential say V_{B}.**Note**: The difference between these two potentials per unit positive charge is called potential difference.

So, the potential difference between the two
points in an electric field is defined as the work done in moving a unit
positive charge from the point of lower potential to the higher potential.

__1.2 Expressions for Potential and Potential Difference__

Consider a
positive charge Q placed in a medium of relative permittivity. Consider a point
P at a distance r from the charge Q. Now, a unit positive charge of 1 c is
placed at point P, there will exist a force of repulsion between the two
charges. This is shown in the Fig 3.

The force of
repulsion is given by,

Now electric
field intensity at point P is the ratio of force to charge at point P. But
charge at P is unit charge,

Now, move the unit charge at point P towards charge Q against the force of repulsion

**Work Done:**

Let the
distance moved by charge at P towards Q be dr and for this work is done against
force of repulsion, given by,

The negative
sign indicates that the work is done against the force of repulsion.

Now, to
find electrical potential at point P, consider that the unit positive charge is
moved from infinity to the point P. hence, total wok done in moving unit
positive charge is from infinity to point P can be obtained by integrating dW
as,

**Note**: But this total work done is nothing but potential at point P.

Thus, as r
increases, potential decreases till it becomes zero at infinity.

**Potential difference :**

Consider point
A at a distance d

_{1}from charge Q. Hence, potential of point A is given by,
While the potential of point B which is at distance d

_{2}from the charge Q is,
Hence, the
potential difference between the points A and B is given by,

We know that
field intensity at a distance 'd' due to charge Q is given by,

While the
potential of the same point is given by,

Substituting V
in expression for E, we can write,

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