Question

Write the definition of electric potential. Calculate the electric potential due to a point charge Q at a distance r from it. Draw a graph between electric potential V and distance r for a point charge Q.

Answer 1

Electric potential is the amount of electric potential energy that a unitary point electric charge would have if located at any point in space, and is equal to the work done by an external agent in carrying a unit of positive charge from the arbitrarily chosen reference point (usually infinity) to that point without any acceleration.

Electric potential due to point charge Q at a distance r is

$V=-{\int }_{\infty }^{r}Edr$

$={\int }_{-\infty }^r\frac{Q}{4\pi {ϵ}_0{r}^2}dr$

$=\frac{Q}{4\pi {ϵ}_{0}r}$