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  4. Two equal -ve 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 poin (2 a, 0) on the x-axis. The charge will :

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Q. Two equal -ve 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 poin $(2 a, 0)$ on the $x$-axis. The charge will :

JIPMERJIPMER 2006Oscillations

Solution:

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Component of force on charge $+Q$ at $P$, along $x$-axis,
$F_{x} =\frac{2 Q q}{4 \pi \varepsilon_{0}\left(a^{2}+x^{2}\right)} \cos \theta$
$=\frac{2 Q q}{4 \pi \varepsilon_{0}\left(a^{2}+x^{2}\right)} \times \frac{x}{\sqrt{a^{2}+x^{2}}}$
$=\frac{2 Q q x}{4 \pi \varepsilon_{0}\left(a^{2}+x^{2}\right)^{3 / 2}}$
Which is not directly proportional to x. So, motion is oscillatory but not SHM.