# What is the formula for electric potential energy of two point charges .how do u derive?

1
by nithees

2014-07-22T18:31:32+05:30

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From coulomb's equation, derive electric field. From that derive electric potential.
From that derive potential energy.

q1 is at A and q2 is at B and AB = r.
force on q2 by q1 =  F = Z * q1 * q2 / r^2
Z =  1 / 4pie epsilon
electric field at B due to q1  = F / q2  = E =  Z q1 / r^2
Electric potential at B due to q1 = Integral E dr    ,  r varies from infinity to AB
= V at B =  - Z q1 / r
Potential Energy at distance AB of both charges : q2 * V at B
Potential Energy in bringing q2 from infinity to B =
q2 ( potential at B - potential at infinity)  = - Z q1 Q2 / r
as potential and P E at infinity are zero.