Question

Two equal negative charges are fixed at points $[0,a]$ and $[0,-a]$ in the $X-Y$ plane. A positive charge $Q$ is released from rest from the point $[2a,0]$. The charge $Q$ will :

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

Answer 1

The correct option is D execute oscillatory motion but not SHM

$F_{net}=F_1\cos \theta +F_2\cos \theta$

$=2F_1\cos \theta$

$=\frac{2\times kqQ}{(a^2+x^2)}\times \frac{x}{\sqrt{a^2+x^2}}$

$2kqQ\frac{k}{(a^2+x^2{)}^{\frac{3}{2}}}$

Its not of form $k^{\prime }{x}^{\prime }$

So, not SHM, but dependent on ${}^{\prime }{x}^{\prime }$ so oscillatory.