Three equal negative charges, `-q_(1)` each form the vertices of and equilateral triangle . A particle of mass m and a positive charge `q_(2)` is constrained to move along a line perpendicular to the plane of triangle and through its center, which at a distance r from each of the negative charges as shown in fig. The whole systen is kept in gravity-free space, Find the time period of vibration of the particle for small displacement from the equilibrium position.

Answer

`2 pi sqrt((4 pi epsilon_(0)mr^(3))/(3q_(1)q_(2)))`

Explanation

`(F_("net"))=3F cos theta =(3kq_(1)q_(2))/(R^(2))(x)/(R )=ma`
or, `a=[(3kq_(1)q_(2))/(4 pi epsilon_(0)mr^(3))] x` (as for small x, R=r)
`T=2 pi sqrt((4 pi epsilon_(0)mr^(3))/(3kq_(1)q_(2))`
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