Two identical metallic spheres $A$ and $B$ when placed at certain distance in air repel each other with a force of $F$. Another identical uncharged sphere $C$ is first placed in contact with $A$ and then in contact with $B$ and finally placed at midpoint between spheres $A$ and $B$. The force experienced by sphere $C$ will be.

Suppose the charge of a proton and an electron differ slightly. One of them is $-e,$ the other is $(e + \Delta e).$ If the net of electrostatic force and gravitational force between two hydrogen atoms placed at a distanced (much greater than atomic size) apart is zero, then $\Delta e$ is of the order of $[$ Given: mass of hydrogen $m_h = 1.67 \times 10^{- 27}\,\, kg]$

Two charges $-\mathrm{q}$ each are fixed separated by distance $2\mathrm{d}$. A third charge $\mathrm{d}$ of mass $m$ placed at the midpoint is displaced slightly by $x (x \,<\,<\, d)$ perpendicular to the line joining the two fixed charged as shown in figure. Show that $\mathrm{q}$ will perform simple harmonic oscillation of time period.  $T =\left[\frac{8 \pi^{3} \epsilon_{0} m d^{3}}{q^{2}}\right]^{1 / 2}$

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

A point charge $q_1$ exerts an electric force on a second point charge $q_2$. If third charge $q_3$ is brought near, the electric force of $q_1$ exerted on $q_2$

Two charges $q$ and $-3q$ are placed fixed on $x-axis$ separated by distance $'d'$. Where should a third charge $2q$ be placed such that it will not experience any force ?