If "`q_(1)+q_(2)=q`" ,then the value of the ratio "`q_(1)/q`" ,for which the force between `q_(1)` and "`q_(2)`" is maximum is

Options

A. 0.25
B. 0.75
C. 1
D. 0.5

Answer

D

Explanation

Let r be the distance between `q_(1)` and `q_(2)`.
According to Coulomb.s law, the force between them is
`F = (1)/(4pi epsilon_(0))(q_(1)q_(2))/(r^(2)) = (1)/(4pi epsilon_(0))(q_(1)(q -q_(1)))/(r^(2)) " "(because q_(1) + q_(2) = q)`
For F to be maximum `(dF)/(dq_(1)) = 0 :. (d)/(dq_(1))[(1)/(4pi epsilon_(0)r^(2))(q_(1)q - q_(1)^(2))] = 0`
`rArr q - 2q_(1) = 0 rArr (q_(1))/(q) = (1)/(2) = 0.5 " "["As " (1)/(4pi epsilon_(0)r^(2)) != 0]`