Assertion : Consider two identical charges placed distance $2d$ apart, along $x-$ axis. The equilibrium of a positive test charge placed at the point $O$ midway between them is stable for displacements along the $x-$ axis.

Reason: Force on test charge is zero

Two point charges placed at a certain distance $r$ in air exert a force $F$ on each other. Then the distance $r'$ at which these charges will exert the same force in a medium of dielectric constant $k$ is given by

There are two metallic spheres of same radii but one is solid and the other is hollow, then

Given below are three schematic graphs of potential energy $V(r)$ versus distance $r$ for three atomic particles : electron $\left(e^{-}\right)$, proton $\left(p^{+}\right)$and neutron $(n)$, in the presence of a nucleus at the origin $O$. The radius of the nucleus is $r_0$. The scale on the $V$-axis may not be the same for all figures. The correct pairing of each graph with the corresponding atomic particle is

Two equal positive point charges are separated by a distance $2 a$. The distance of a point from the centre of the line joining two charges on the equatorial line (perpendicular bisector) at which force experienced by a test charge $q_0$ becomes maximum is $\frac{a}{\sqrt{x}}$. The value of $x$ is $................$

When the distance between the charged particles is halved, the force between them becomes