12.3 Potential Due to Point Charge

  Electrostatics

Derivation of expression for potential due to point charge $Q,$ at a point which is at a distance are from the point charge

From definition of potential $$V = \frac{{{W_{ext\left( {\infty \to p} \right)}}}}{{{q_o}}} = \frac{{ - \int\limits_\infty ^r {\left( {{q_0}\overrightarrow E } \right).d\overrightarrow r } }}{{{q_o}}} = - \int\limits_\infty ^r {\overrightarrow E } .\;\overrightarrow {dr} $$$$ \Rightarrow \quad V = - \int\limits_\infty ^r {\frac{{KQ}}{{{r^2}}}\left( { - dr} \right)} \cos \;180^\circ = \frac{{KQ}}{r}$$