Two metallic balls of radii R 1 and R 2 are kept in vacuum at a large distance compared to their radii. Find the ratio of the charges on the two balls for which electrostatic energy of the system is minimum. What is the potential difference between the two balls for this ratio? Total charge of the balls is constant. Neglect the interaction energy. (charge distribution on each ball is uniform)
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Sol.
Let total charge is Q and charge on ball (1) is q so charge on 2 nd ball = Q – q
Now x >>> R 1 and R 2 so we can neglect potential energy of interaction,
So, total energy = 
+ 
= E
For E to be minimum: 
= 0
⇒ 
= 0
⇒ 
= 
⇒ q = 
and Q – q = 
So ratio of charge = 
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