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

1
by nithees

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by nithees

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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.

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.