Two spheres of electric charges +2 nC and -8 nC are placed at a distance d apart. If they are allowed to touch each other, what is the new distance between them to get a repulsive force of same magnitude as before?

Options

A. `(d)/(2)`
B. d
C. `(3d)/(4)`
D. `(4d)/(3)`

Answer

C

Explanation

Force on each sphere
`=(kq_(1)q_(2))/(r^(2))=(-16k)/(d^(2)) xx 10^(-18)N`
When both the spheres are allowed to touch each other, the charges get redistributed.
`"Charge on each sphere"=((2-8))/(2)nC=-3 nC`
`"Force on each sphere"=(K(-3 nC)^(2))/(r^(2))=(9k)/(r^(2)) xx 10^(-18)N`
According to the question
`(16k)(d^(2)) xx 10^(-18)=(9k)/(r^(2)) xx 10^(-18), r=(3)/(4) d`