12.0 Electric Potential

  Electrostatics

In electrostatics field, the electric potential (due to some source charges) at a point $P$ is defined as the work done by external agent in taking a unit point positive charge from a reference charge point (generally taken at infinity) to that point $P$ without changing its kinetic energy..

Mathematical representation :

If ${{{\left( {{W_{\infty \; \to P}}} \right)}_{ext}}}$ is the work required in moving a point charge $q$ from infinity to a point $P,$ the electric potential of the point $P$ is $${\left. {{V_P}\frac{{{{\left( {{W_{\infty \; \to P}}} \right)}_{ext}}}}{q}} \right]_{\Delta K = 0}} = \frac{{{{\left( { - {W_{elc}}} \right)}_{\infty \; \to P}}}}{q}$$ Note:

(I) ${{{\left( {{W_{\infty \; \to P}}} \right)}_{ext}}}$ can also be called as the work done by external agent against the electric force on a unit positive charge due to the source charge.

(II) Write both $W$ and $q$ with proper sign.