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 $................$

Force between two identical spheres charged with same charge is $F$. If $50\%$ charge of one sphere is transferred to second sphere then new force will be

A charge $q$ is placed at the centre of the line joining two equal charges $Q$. The system of the three charges will be in equilibrium, if $q$ is equal to

Two small spherical balls each carrying a charge $Q = 10\,\mu C$ ($10\, micro-coulomb$) are suspended by two insulating threads of equal lengths $3\, m$ each, from a point fixed in the ceiling. It is found that in equilibrium threads are separated by an angle $120^o$ between them, as shown in the figure. What is the tension in the threads (Given : $\frac{1}{{\left( {4\pi {\varepsilon _0}} \right)}} = 9 \times {10^9}\,Nm/{C^2}$)

A paisa coin is made up of $\mathrm{Al - Mg}$ alloy and weighs $0.75\, g$ It is electrically neutral and contains equal amounts of positive and negative charge of magnitude $34.8$ $\mathrm{kC}$. Suppose that these equal charges were concentrated in two point charges separated by :

$(i)$ $1$ $\mathrm{cm}$ $(\sim \frac{1}{2} \times $ diagonal of the one paisa coin $)$

$(ii)$ $100\,\mathrm{m}$ $(\sim $ length of a long building $)$

$(iii)$ $10^6$ $\mathrm{m}$ (radius of the earth).

Find the force on each such point charge in each of the three cases. What do you conclude from these results ?

Force between $A$ and $B$ is $F$. If $75\%$ charge of $A$ is transferred to $B$ then force between $A$ and $B$ is