Question

Two indentical charges $+$Q are kept fixed some distance apart. A small particle P with charge q is placed midway between them. If P is given a small displacement $\Delta$, it will undergo simple harmonic motion if

• A. q is positive and $\Delta$ is along the line joining the charges
• B. q is positive and $\Delta$ is perpendicular to the line joining the charges
• C. q is negative and $\Delta$ is perpendicular to the line joining the charges
• D. q is negative and $\Delta$ is along the line joining the charges

Answer 1

Answer: (A), (C)

The correct options are
A q is positive and $\Delta$ is along the line joining the charges
C q is negative and $\Delta$ is perpendicular to the line joining the charges

$\left(A\right)$ q is $+$ve then there will be net repulsive force which will send the charge particle back to its original position so it will be an S.H.M.
$\left(C\right)$ q is $-$ve then there will be net attractice force which will send the charge particle back to its original position so it will be an S.H.M.