A charge fo magnitude Q is divided into two parts q and `(Q - q)` such that the two parts exert maximum force on each other. Calculate the ratio `Q//q`.

Answer

2

Explanation

Here, `F = (1)/(4pi in_(0)) (q(Q-q))/(r^(2))`
As Q and r are fixed, so F is a function of q
Force F will be maximum, only if `(dF)/(dq) = 0`
or `(1)/(4pi in_(0)) (d)/(dq) [q (Q - q)] = 0`
or `(d)/(dq) [q(Q - q)] = 0 or q(-1) + (Q - q) = 0`
or `Q - 2q = 0 or Q = 2q`
`(Q)/(q) = 2`