Two identical conducting balls having positive charges q1 and q2 are separated by a distance r. If they are made to touch each other and then separated to the same distance, the force between them will be
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When they are made to touch each other the net charge will be distributed between them, hence charge
q = (q₁+q₂)/2
we know that force between two charge particles is given by,
F = (1/4πε₀)(q₁q₂)/r²
where
q₁ = q₂ = q = (q₁+q₂)/2
r = distance between them
hence the force,
F = (1/4πε₀)(qq)/r²
=> F = (1/4πε₀)(q₁+q₂)²/4r²
=> F = (1/16πε₀)(q₁+q₂)²/r²
which is the required expression.
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