Electrostatic potential

due to a point charge


1)Suppose a source charge +Q is the position O.



Determine potential at L

2)Now we have to calculate electric potential at L at a distance r from O.

3)Say a unit positive charge is at A position at a distance x, from the O

Therefore electric force at A is


4)By using an external force unit positive charge is brining from A to B position at a distance dx, then work done,


   dw   =  force × distance

[ here negative sign appears because dx<0, and work dw is positive ]

5) Now according to the definition of electrostatic potential, potential is the work done on carrying a unit positive charge 

from infinity to a distance r.

6) So total work done by the external force is










This is the potential at a distance r from the source charge Q.



 

Graphical relation between E and V


We know that

Electrostatic potential




Electrostatic field



Thus  we see that



From the above 2.12 and 2.21 we can obtain the graphical relation between E and V with distance r.