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. `1xx10^(-5)N`
B. `2xx10^(-5)N`
C. `1.5xx10^(-5)N`
D. `3xx10^(-5)N`

Answer

C

Explanation

If same charges on spheres A and B are q,
Force, `F=(1)/(4pi epsilon_(0))(q^(2))/(r^(2))=3xx10^(-5)N`
Charge on A and C after touching,
`q'_(A)=q_(C)=(q)/(2)`

`therefore" Net force on C, F"=F_(A)+F_(B)`
`therefore" "F=(1)/(4pi epsilon_(0))((q//2)(q//2))/((r//2)^(2))-(1)/(4pi epsilon_(0))((q//2)xxq)/((r//2)^(2))`
`=((1)/(4piepsilon_(0)r))(q^(2))/(r^(2))-(1)/(2)((1)/(4piepsilon_(0)))(q^(2))/(r^(2))=(1)/(2)((1)/(4piepsilon_(0)).(q^(2))/(r^(2)))`
`=(3xx10^(-5))/(2)N=1.5xx10^(-5)N`