# Electric Potential Due To Single Charge Or Point Charge

let us discuss and derive the electric potential due to single charge or point charge. We will calculate electric potential at any point P due to a single point charge +q at O ;where OP=r

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

= -Edx

Total work done in moving unit + charge from ∞ to the point P is

W= -∫Edx

=∫ -1/4πε0q/x2dx

= -q/4πε0∫x-2 dx

= -q/4πε0[-1/x]

W= q/4πε0[1/r-1/∞]

=q/4πε0r

This is the potential at P i.e

V=W=q/4πε0r

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.

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