The forces exerted by the charged particles on each other are equal in magnitude but opposite in direction.
Let us consider a few charges distributed in space. Let these charges be taken together to form a system of charges.
Now consider an external charge q to be placed at B. The charge q will experience a force due to the system of charges.
Thus a force is required to hold charge q at B. Suppose we want to move the charge from point
B to A.
Then, work has to be done against the force acting on B due to the system of charges.
This work done per unit charge ( W/q) is the potential difference between A and B. It is denoted by V(A)-V(B). Mathematically
V(A) -V(B) = W/q
What do we mean by V(A) and V(B)?
V(A) and V(B) are called the potentials at A and B.
As we have a choice to select a point as 0 on the x-axis, we can select 0 anywhere on the axis, but the distance between two points x₁ and x₂, remains the same.
Similarly, we can assign the potential 0 at any point on the charges system. Generally, a point at a very large distance from all charges is assigned zero potential.
The assumption is that the potential at infinity from the system of charges is 0.
POTENTIAL AT A POINT:
The potential at point A is defined as work done in bringing a unit charge from infinity to that point.
Definition
Mathematically it can be written as
V = W/q
Implies W = Vq .
This work done is stored in the charge as electric potential energy.
Thus the electric potential energy increases by Vq on charge q when brought from infinity to a point P.
The SI unit of potential is named in honour of Italian physicist Alessandro Voltas of the 18th century. It is volt. The symbol for volt is V.
Definition: The potential difference between two points A and B is said to be one volt if one joule of work is done in bringing one coulomb of charge from
A to B.