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. `1xx10^(-5)N`
B. `3xx10^(-5)N`
C. `2xx10^(-5)N`
D. `5xx10^(-5)N`

Answer

B

Explanation

`F=(1)/(4 pi f_ c).(q.q)/(r^2)`
`F=(4)/( 4 pi in_0).(q^2)/(r^2)=3xx10^(-5) N`.

`F_(CA)=(1)/(4pi epsilon_0),((q)/(2)xx(q)/(2))/((( r)/(2))^2)`
`rArr (1)/(4 pi epsilon_0).(q^2)/(r^2)`
`F_(CA)=(1)/(4 pi epsilon_0).((q)/(2)xxq)/((( r)/(2))^2)=(2q)/( r^2)`
`F^(1)=F_(CB) - F_(CA)`
`=(1)/(4pi epsilon_0).(2q^2)/( r^2) -(1)/(4 pi epsilon_0).(q^2)/(r^2)`
`F^(1)=F`
`F^(1)=3 xx 10^(-5) N`.