two similar point charge + q are kept on x- axis at (-a,0)& (a,0) and another charge -Q of mass m Is kept at origin .If -Q si slightly displaced along y- axis & released them its time period of oscillation is -

Options

A. `2pisqrt((piepsi_(0)ma^(3))/(2Qq))`
B. `2pisqrt((piepsi_(0)ma^(3))/(Qq))`
C. `2pisqrt((2piepsi_(0)ma^(3))/(Qq))`
D. none of these

Answer

C

Explanation

`=-2(kQq)/((a^(2)+y^(2))sqrt(a^(2)=y^(2)))`
`f_("net") =-(Qqy)/(2piin_(0)(a^(2)+y^(2))^(3//2))`
for y ltlta
`F_("net")=-(Qqy)/(2piepsi_(0)a^(3))`
` a=(F_("net"))/(m)=-(Qq)/(2piepsi_(0)ma^(3))=-omega^(2)y`
`omega ^(2)=(Qq)/(2piepsi_(0)ma^(3))`
`omega =sqrt((Qq)/(2 piepsi_(0)ma^(3)))`
`T=(2pi)/(omega)=2pi sqrt((2 pi epsi_(0)ma^(3))/(Qq))`