Two charged identical metal spheres A and B repel each other with a force of `3 xx 10^(-8) N` Another idenitcal uncharged sphere C is touhced with sphere A and then it is placed mid way between A and B. Then the magnitude of net force on C is

Options

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

Answer

b

Explanation

Sphere A and B have the same charge of same nature when uncharged sphere C is touch with sphere A, then charge is transferred to C and this charge is equally divided between two spheres.

Let initially the charge on sphere A and B is q.
Initially, the repelling force between charged spheres A and B `= 3 xx 10^(-5) N`
When, sphere C, is placed between charged spheres A, and B then
the force between A and C
`F_(AC) = (k(q)/(2) xx q//2)/((r//2)^(2))`
Similarly, between B and C
`F_(ac) = (kq xx q//2)/((r//2)^(2))`
The magnitude of net force on C,F `= F_(BC) = F_(ac)`
Also `F = (kq xx q)/(t^(2)) = 3 xx 10^(-5) N`
So, `(F)/(F_(BC) - F_(AC)) = ((kq^(2) // r^(2)))/(k[(q xx q//2)/((r//2)^(2)) - (q//2 xx q//2)/((r//2)^(2))])`
Here, `F = 3 xx 10^(-5) N, F_(BC) - F_(AC) = F'`
`(3 xx 10^(-5))/(F') = (1)/(2 -1) = (1)/(1) = 1`
`:. F' = 3 xx 10^(-5) N`