Question

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 $(2a,0)$ on the $x$-axis. The charge will :

• A. execute SHM about the origin
• B. move to the origin and remain at rest
• C. move to infinity
• D. execute oscillatory but not SHM

Answer 1

Answer: (D)

Component of force on charge $+Q$ at $P$, along $x$-axis,
$F_x=\frac{2Qq}{4\pi {\epsilon }_0\left(a^2+x^2\right)}\cos \theta$
$=\frac{2Qq}{4\pi {\epsilon }_0\left(a^2+x^2\right)}\times \frac{x}{\sqrt{a^2+x^2}}$
$=\frac{2Qqx}{4\pi {\epsilon }_0{\left(a^2+x^2\right)}^{3/2}}$
Which is not directly proportional to x. So, motion is oscillatory but not SHM.