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 `q_(1) and q_(2)` is
` F = (1)/( 4 pi epsilon_(0)) (q_(1) q_(2))/(r^(2)) = (1)/( 4 pi epsilon_(0)) (q_(1) (q - q_(1)))/( r^(2)) ` (`:. q_(1) + q_(2) = q`)
For F to be maximum ` (dE)/( dq_(1)) = 0` , as q and r are constants
`:. (d) /(dq_(1)) [ (1)/( 4 pi epsilon_(0) r^(2)) (q_(1) q - q_(1)^(2)) ] = 0 `
`q = 2 q_(1) = 0 [ As (1)/( 4 pi epsilon_(0) r^(2)) ne 0]" " :. (q_(1))/( q) = (1)/(2) = 0 . 5`