Solution
= Solution
The <image charge for a grounded conducting sphere> is $-qa/d$ at radius $a^2/d$. With symmetric real charges, their exact force-balance equation has a solution close to $d/a=8$. Holding potential $V$ adds force $qaV/d^2$ to the grounded result, approximately $qV/(64a)$ at that separation.
Full derivation: <past-exam-of-the-physics-b-course-of-the-university-of-cambridge/2010/paper-2a/section-b/b9/solution>.