Electric Potential Due To Single Charge Or Point Charge
Electric potential at P is the amount of work done in carrying a unit positive charge from ∞ to P.
At any point A on the line joining OP ,where OA=x,the electric intensity is E=1/4πε0q/x2 along OA produced (try to make the figure yourself).
Amount of work done in moving a unit positive charge from A to B where (AB=dX) is
dW=E.dx=Edx cos 1800
Total work done in moving unit + charge from ∞ to the point P is
= -q/4πε0∫x-2 dx
This is the potential at P i.e
When q is positive ,potential V is positive and when q is negative,potential V is negative i.e a positive charge produces a positive electric potential and negative charge produces a negative electric potential.
This is the electric potential due to single charge or point charge.