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(D) Let the position of the positive charge $Q$ be at $(x, 0)$. The distance between each negative charge $-q$ and the positive charge $Q$ is $r = \sq

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execute oscillatory but not simple harmonic motion.

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(D) Let the position of the positive charge $Q$ be at $(x, 0)$. The distance between each negative charge $-q$ and the positive charge $Q$ is $r = \sqrt{x^2 + a^2}$.The magnitude of the electrostatic force $F$ exerted by each negative charge on $Q$ is $F = \frac{1}{4 \pi \varepsilon_0} \frac{qQ}{x^2 + a^2}$.The components of these forces perpendicular to the $x$-axis cancel each other out,while the components along the $x$-axis add up.The net restoring force $F_{	ext{net}}$ is given by:$F_{	ext{net}} = -2F \cos 	heta = -2 \left( \frac{1}{4 \pi \varepsilon_0} \frac{qQ}{x^2 + a^2} ight) \left( \frac{x}{\sqrt{x^2 + a^2}} ight)$$F_{	ext{net}} = -\frac{2qQ}{4 \pi \varepsilon_0} \frac{x}{(x^2 + a^2)^{3/2}}$Since $F_{	ext{net}} \propto -x$ is not strictly true for all $x$ (it is only true for $x \ll a$),the restoring force is not linear. Therefore,the motion is oscillatory but not simple harmonic.

Two equal negative charges are fixed at the points $(0, a)$ 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 $Q$ will

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