Define electric potential and explain it. Write its $\mathrm{SI}$ unit and give its other units.

The work required to be done against the electric field to bring a unit positive charge from infinite distance to the given point in the electric field is called the electrostatic or electric potential at that point. It is indicate by ' $\mathrm{V}$ '.

Consider a positive charge $\mathrm{Q}$ at the origin $\mathrm{O}$ and point $\mathrm{P}$ at certain distance and point $\mathrm{R}$ at infinite distance from its electric field.

Work done in brining a unit positive charge from infinity to the point $\mathrm{P}$ is the potential energy of that charge.

$\therefore$ Potential energy at $\mathrm{P}$ is $\mathrm{U}_{\mathrm{P}}$ and potential energy at point $\mathrm{R}$ is $\mathrm{U}_{\mathrm{R}}$ but $\frac{\mathrm{U}_{\mathrm{P}}-\mathrm{U}_{\mathrm{R}}}{q}$ is called electric potential difference between these points,

$\therefore \mathrm{V}_{\mathrm{P}}-\mathrm{V}_{\mathrm{R}}=\frac{\mathrm{U}_{\mathrm{P}}-\mathrm{U}_{\mathrm{R}}}{q}$

where $V_{P}$ and $V_{R}$ are potential at point $P$ and $R$.

Absolute value of electric potential has no importance only the difference in potential is important.

If we take potential to be zero at infinity then from equation $(1)$,

$\mathrm{V}_{\mathrm{P}}=\frac{\mathrm{U}_{\mathrm{P}}-\mathrm{U}_{\mathrm{R}}}{q}$

Hence, work done by an external force in bringing a unit positive charge without acceleration from infinity to a point is the electrostatic potential at that point.