ELECTRIC (OR ELECTROSTATIC) POTENTIAL
What do you understand by electric potential Explain. Give dimensional formula and SI unit of electric potential. What is the unit of electric potential in CGS system? Establish the relation between SI and CGS units of electric potential.
Electric potential: Electric potential at a point in the electric field is defined as the work done in moving a unit positive test charge from infinity to that point in the electric field of the source charge.
Expression for Electric potential:
Electric potential at a point in an electric field is also defined as the electric potential energy per unit charge.
Let U be the electrostatic potential energy at a point (say B) in the electric field. Then, the electric potential at that point in the electric field is given by
$V = \frac{U}{q_0} = \frac{W}{q_0}...(1)$
But electric potential energy of test charge $q_0$ at point (say B) in the electric field is given by
$U = -q_0 \int_{\infty}^B \vec{E} \cdot d\vec{r}$
$\therefore$ Electric potential at that point (say B) in the electric field is given by
$V = \frac{U}{q_0} = - \int_{\infty}^B \vec{E} \cdot d\vec{r} ...(2)$
Electric potential is a scalar quantity as it is the ratio of two scalar quantities (work or potential energy and charge).
Dimensional formula for Electric Potential
$\frac{[\text{Work}]}{[\text{Charge}]} = \frac{[\text{Work}]}{[\text{Current} \times \text{Time}]}$
$= \frac{[ML^2T^{-2}]}{[AT]} = [ML^2T^{-3}A^{-1}]$
SI Unit of Electric Potential is volt (V)}
Since
$V = \frac{U}{q_0}$
$\therefore$ $1volt= \frac{1 \text{ joule (J)}}{1 \text{ coulomb (C)}} = 1 \text{ JC}^{-1}$
Thus, electric potential at a point in the electric field is one volt if one joule of work is done in moving one coulomb of charge from infinity to that point in the electric field.
In CGS system, unit of electric potential is stat volt.
1 stat volt = 1 erg/1 stat coulomb
Electric potential at a point in the electric field is one stat volt if one erg of work is done in moving one stat coulomb charge from infinity to that point in the electric field.
Relation between volt and stat volt
1 volt = $\dfrac{1 \text{ joule}}{1 \text{ coulomb}} = \dfrac{10^7 \text{ erg}}{3 \times 10^9 \text{ esu}} = \dfrac{1}{300}$ stat volt