Two equal charges `q` are kept fixed at a and `+a` along the `x`-axis. A particle of mass `m` and charge `q/2` is brought to the origin and given a small displacement along the `x`-axis then

Options

A. the particle executes oscillartory motion
B. the particle remains stationary
C. the partiel executes, SHM along `x`-axis
D. the particle executes SHM along `y`-axis

Explanation

(c) From coulomb's law,

`F=1/(4 epsilon_(0))(q_(1)q_(2))/(r^(2))`
`F=1/(4pi epsilon_(0))(qxxq/2)/((a+x)^(2))-1/(4piepsilon_(0)).(qxxq/2)/((a-x)^(2))`
`=1/(4piepsilon_(0))(q^(2))/2[1/((a+x)^(2))-1/((a-x)^(2))]`
`=1/(4piepsilon_(0).(q^(2))/2 [-(4ax)/((a^(2)-x^(2))^(2))]`
When `x lt lt a`, then
`F=-(2q^(2))/(4piepsilon_(0)a^(3))ximpliesF prop -x`
Hence SHM isaklong `x`-axis.