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1. Electric Charges and Fields
normal
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 points $[2a, 0]$ on the $x-$axis . The charge $Q$ will
A
execute simple harmonic motion about the origin
B
move to the origin and remain at rest
C
move to infinity
D
execute oscillatory but not simple harmonic motion.
Solution
The net force is given as,
$F_{n}=2 F \cos \theta$
$=2 \times \frac{1}{4 \pi \varepsilon_{0}}\left(\frac{-q Q}{a^{2}+x^{2}}\right) \times\left(\frac{x}{\left(a^{2}+x^{2}\right)^{\frac{1}{2}}}\right)$
Thus, the restoring force is not linear, So, the motion will not be simple harmonic motion but the motion will be oscillatory.
Standard 12
Physics
