Question

Two identical conducting spheres 1 and 2 carry equal amounts of charge and are ficed apart at a certain distance larger than their diameters. The spheres repel each other with an electrical force of 88mN. A thired identical sphere 3, having an insulating handle and initially uncharged, is touched first to sphere 1 and then to sphere 2 and finally removed. Find the force between spheres 1 and 2 as shown if Figure.
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Answer 1

Initial force between 1 and 2 is `F=kq^(2)//r^(2)=88mN`. Charge on 1 after 3 is touched with 1 is `q//2`. Same charge will be on 3 also. Charge on 2 after 3 is touched with 2 is
`(q+(q//2))/(2)=(3q)/4`
Now, force between 1 and 2 in situation (d) is
`F=(k(q//2)(3q//4))/(r^2)=(3 kq^(2))/(8r^2)=3/8xx88=33mN`.