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(D) The charge $Q$ is attracted by both negative charges $-q$ located at $(0, a)$ and $(0, -a)$. Due to symmetry,the net force on $Q$ will always be d

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execute oscillatory motion but not $SHM$

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(D) The charge $Q$ is attracted by both negative charges $-q$ located at $(0, a)$ and $(0, -a)$. Due to symmetry,the net force on $Q$ will always be directed towards the origin along the $x$-axis.Let the charge $Q$ be at a distance $x$ from the origin $O$ on the $x$-axis. The distance between $Q$ and each charge $-q$ is $r = \sqrt{a^2 + x^2}$.The magnitude of the electrostatic force exerted by each charge $-q$ on $Q$ is $F = \frac{1}{4 \pi \varepsilon_0} \frac{qQ}{a^2 + x^2}$.The resultant force $F_R$ acting on $Q$ is the sum of the $x$-components of these two forces:$F_R = 2 F \cos 	heta$,where $\cos 	heta = \frac{x}{r} = \frac{x}{\sqrt{a^2 + x^2}}$.Substituting the values:$F_R = 2 \left( \frac{1}{4 \pi \varepsilon_0} \frac{qQ}{a^2 + x^2} ight) \left( \frac{x}{\sqrt{a^2 + x^2}} ight) = \frac{2qQ}{4 \pi \varepsilon_0} \frac{x}{(a^2 + x^2)^{3/2}}$.Since the restoring force $F_R$ is not proportional to the displacement $x$ (i.e.,$F_R 
eq -kx$),the motion is oscillatory but not simple harmonic $(SHM)$.

Two equal negative charges $-q$ are fixed at points $(0, -a)$ and $(0, a)$ in the $x-y$ plane. $A$ positive charge $Q$ is released from rest at a point $(2a, 0)$. The charge $Q$ will

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