ELECTRIC POTENTIAL AT A POINT DUE TO POINT CHARGE

ELECTRIC POTENTIAL AT A POINT DUE TO POINT CHARGE:-

We can derive this potential at point due to point charge by two methods one is by using gausses law and other is by general methods

By using gausses law

consider a charge. In order to calculate electric flux by gausses law we have to draw 

a Gaussian surface consider a spherical Gaussian surface as shown in fig. Charge is enclosed in it.

by gausses law we know that

ɸ=q/ε_{o       ------(ix)}

_{equate (viii) and (ix) we get}

E(4πr²)=q/ε_o

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similarly we can prove this by general method

By general method

Consider a point charge +q around which electric field is directed in outward (radial outward) direction as shown in fig. We place another test charge +q_{o and it move from B to A with some force against the direction of electric field. From fig we see that}

  r_A= distance of point A from central charge q

  r_B= distance of point B from central charge q 

  r = distance of point P from central charge q 

∆r=distance between point A and B

  ∆r=r_{B -}  r_{A  ------(i)}

_or  r_{B =} ∆r + r_A------(ii)

also from fig we find that

_CONCLUSION:-

Electric potential V depends

• directly upon magnitude of charge
• inversely upon distance from central charge