Two small identical metal balls of radius rare at a distance a `(a lt lt r)` from each other and are charged, one with a potential `V_(1)` and the other with a potential `V_(2)`. The charges on the balls are:

Options

A. `q_(1)=V_(1)a,q_(2)=V_(2)a`
B. `q_(1)=V_(1)r,q_(2)=V_(2)r`
C. `q_(1)=((V_(1)+V_(2))/2)a,q_(2)=((V_(1)+V_(2))/2)r`
D. `q_(1)=-r/a(rV_(2)-aV_(1),q_(2)=)-r/a(rV_(1)-aV_(2))`

Answer

D

Explanation

`V_(1)=1/(4pi epsilon_(0))[(q_(1))/r+(q_(2))/a]` and `V_(2)=1/(4piepsilon_(0))[(q_(2))/r+(q_(1))/a]`
After sovling above equations, and neglecting `r^(2)` in comparison to a we get
`q_(1)=-r/a(rV_(2)-aV_(1)`,
and `q_(2)=-r/a(rV_(1)-aV_(2))`