We define potential energy of a test charge q in terms of the work done on the charge q. This work is proportional to q, since the force at any point is qE, where E is the electric field at that point due to the given charge configuration. It is, therefore, convenient to divide the work by the amount of charge q, so that the resulting quantity is independent of q.
Potential Difference :
The potential difference between two points in an electric field is defined as the amount of work done in moving a unit positive charge from one point to the other against the electric force.
The unit of potential difference is volt.
Work done by external force in bringing a unit positive charge from point R to P as shown in fig.
Work W(RP)= V(P) – V(R) = [U(P) – U(R)]/q
where V(P) and V(R) are the electrostatic potentials at P and R, respectively.
Electric Potential :
The electric potential in an electric field at a point is defined as the amount of work done in moving a unit positive charge from infinity to that point against the electric forces.
The unit of potential is volt.
If, we consider the potential to be zero at infinity, then
Work done by an external force in bringing a unit positive charge from infinity to a point = electrostatic potential (V) at that point.
Work W∞ p= V(P) – V(∞) = [U(P) – U(∞)]/q
or W∞ p= V(P) = U(P) /q
In other words, the electrostatic potential (V) at any point in a region with electrostatic field is the work done in bringing a unit positive charge (without acceleration) from infinity to that point.
1 Volt :
The potential difference between two points is 1 volt if 1 joule of work is done in moving 1 Coulomb of charge from one point to another against the electric force.
