Two point charges A and B, having charges +Q and -Q respectively, are placed at certain distance apart and force acting between them is F, if `25%` charge of A is transferred to B, then force between the charges becomes:

Options

A. `(4F)/(3)`
B. F
C. `(9F)/(16)`
D. `(16F)/(9)`

Answer

C

Explanation

In case I :

`F = -(1)/(4pi epsilon_(0))(Q^(2))/(r^(2))` …(i)
In Case II :
`Q_(A) = Q - (Q)/(4), Q_(B) = -Q + (Q)/(4)`
`:. F. = (1)/(4pi epsilon_(0)) ((Q-(Q)/(4))(-Q + (Q)/(4)))/(r^(2))`
`= (1)/(4pi epsilon_(0)) (((3)/(4)Q)((-3)/(4)Q))/(r^(2)) = -(1)/(4pi epsilon_(0))(9)/(16)(Q^(2))/(r^(2))` ...(ii)
From equations (i) and (ii),
`F. = (9)/(16)F`