Find the potential energy associated with a charge q if it were present at the point P with respect to the set-up of two charged spheres arranged as shown. Here O is the mid-point of the line `O_(1)O_(2)`.

Explanation

`O_(1)P=sqrt(r^(2)+(a+b)^(2))`
`O_(2)P=sqrt(r^(2)+(b+a)^(2))`
The potential energy associated with charge q at point P is
`V=(q)/(4pi epsilon_(0)) ((Q_(1))/(O_(1)P)+(Q_(2))/(O_(2)P))`
`=(q)/(4pi epsilon_(0))((Q_(1))/(sqrt(r^(2)+(a+b)^(2)))+(Q_(2))/(sqrt(r^(2)+(b+a)^(2))))`