Two equal negative charges - q are fixed at the point (0, a) and (0, - a) on the y-axis. A positive charge Q is released from rest at the point (2a, 0) on the x-axis. The charge wil

execute SHM about the origin

move to the origin and remain at rest

move to infinity

execute oscillatory but not SHM

Solution

execute oscillatory but not SHM

Component of force on charge of + Q at P, along x-axis,

F_x = $\frac{2 Q q}{4 π ε_{o} (a^{2} + x^{2})} \times \frac{x}{\sqrt{a^{2} + x^{2}}}$

= $\frac{2 Qq x}{4 {πε}_{o} (a^{2} + x^{2})} \times \frac{x}{\sqrt{a^{2} + x^{2}}}$

= $\frac{2 Qqx}{4 {πε}_{0} (a^{2} + x^{2})^{3 / 2}}$

Which is not directly proportional to x. So, motion is oscillatory but not SHM.

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