Two equal positive charges $Q$ are fixed at points $(a, 0)$ and $(-a, 0)$ on the x-axis. An opposite charge $-

Question

Two equal positive charges $Q$ are fixed at points $(a, 0)$ and $(-a, 0)$ on the x-axis. An opposite charge $-q$ at rest is released from a point $(0, y)$ on the y-axis. The charge $-q$ will:

Accepted Answer

The charge $-q$ experiences attractive forces from both positive charges $+Q$. The horizontal components of these forces cancel out, while the vertical components add up to provide a net restoring force directed towards the origin. The magnitude of this force is $F_{net} = \frac{2kQqy}{(a^2 + y^2)^{3/2}}$. For Simple Harmonic Motion (SHM), the restoring force must be directly proportional to the displacement ($F \propto -y$). Here, the force is proportional to $y$ only if $y \ll a$ (small oscillations). For general release points, the force is non-linear with respect to distance. Therefore, the charge executes oscillatory periodic motion, but it is not SHM. (See NCERT Physics Class 12, Chapter 1).

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