Two identical conducting spheres, fixed in space, attract each other with an electrostatic force of `0.108 N` when separated by `50.0 cm`, centre-to-centre. A thin conducting wire then connects the spheres. When the wire is removed, the spheres repel each other with an electrostatic force of `0.0360 N`. What were the initial charges on the spheres?

Explanation

Let `q_(1) and -q_(2)` be the initial charges.
be the initial charges.
`F = (K q_(1) q_(2))/(r^())`
`0.018 = (9xx10^(9) q_(1) q_(2))/((0.5)^(2))`
`q_(1) q_(2) = 3xx10^(-12)`
When they are connected and removed, they share equal chrges.
When they are connected and removed, they share equal charges.
`F = K((q_(1)-q_(2))/(2) ((q_(1)-q_(2))/(2)))/(r^(2))`
`0.036 = 9xx10^(9) ((q_(1) - q_(2))/(2))^(2)/(0.5)^(2)`
`(q_(1) - q_(2))^(2)= 4xx10^(-12)`
`q_(1) - q_(2) = 2xx10^(6)` ...(i)
As `(q_(1) + q_(2)) = (q_(1) - q_(2))^(2) + 4q_(1) q_(2)`
`= 4xx10^(-12)+4xx3xx10^(-12)`
`(q_(1) + q_(2))^(2) = 16xx10^(-12)`
`q_(1) + q_(2) = 4xx10^(-6)`
Solving (i) and (ii)
`q_(1) = 3xx10^(-6) C, q_(2) = 10^(-6)C`