There are two charged identical metal spheres A and B repel each other with a force `3xx10^(-5)N`. Another identical uncharged sphere C is touched with A and then placed at the mid-point between A and B. Net force on C is

Options

A. `1 xx 10^(-5) N`
B. `2 xx 10^(-5) N`
C. `1.5 xx 10^(-5) N`
D. `3 xx 10^(-5) N`

Answer

D

Explanation

Let q be the charge on each metal spheres A and B respectively and r is distance between them, then
`F = (q xx q)/(4pi epsilon_(0)r^(2)) = 3 xx 10^(-5) N` ….(i)
After contact, charge on C = charge on `A = (q)/(2)`
Net force on `C = F_(BC) - F_(AC)`
`= (q(q//2))/(4pi epsilon_(0)(r//2)^(2)) - ((q//2)(q//2))/(4pi epsilon_(0)(r//2)^(2)) = (q^(2))/(4pi epsilon_(0)r^(2)) = 3 xx 10^(-5)N` (Using (i))