Two charged metallic spheres of same size repel each other by a force $F$. They are now touched with each other and are then separated to same initial distance. Now the force of repulsion is $F\text{'}$. Which of following are possible ?

In which of the following figures, electric field at point $O$ is non-zero?

A few electric field lines for a system of two charges $Q_1$ and $Q_2$ fixed at two different points on the $x$-axis are shown in the figure. These lines suggest that

Two nonconducting solid spheres of radii $R$ and $2R$ having uniform volume charge densities ${\rho }_1$ and ${\rho }_2$, respectively, touch each other. The net electric field at a distance $2R$ from the centre of the smaller sphere, along the line joining the centre of the spheres, is zero. The ratio $\frac{{\rho }_1}{{\rho }_2}$ can be:

Consider a uniform spherical charge distribution of radius $R_1$ centred at the origin $O$. In this distribution, a spherical cavity of radius $R_2$, centred at $P$ with distance $OP =a =R_1 –\mathit{ }{R}_2$ (see figure) is made. If the electric field inside the cavity at position $\stackrel{\mathit{\rightharpoonup }}{\mathit{r}}$ is $\stackrel{\rightharpoonup }{E }\left(\stackrel{\rightharpoonup }{r}\right)$, then the correct statement(s) is(are) 

The figures below depict two situations in which two infinitely long static line charges of constant positive line charge density $\mathrm{\lambda }$ are kept parallel to each other. In their resulting electric field, point charges $q$ and $-q$ are kept in equilibrium between them. The point charges are confined to move in the $x$-direction only. If they are given a small displacement about their equilibrium positions, then the correct statement(s) is (are):

A cubical region of side a has its centre at the origin. It encloses three fixed point charges, $-q$ at $\left(0, -\frac{a}{4}, 0\right), +3q$ at $\left(0, 0, 0\right), -q$ at $\left(0, +a/4, 0\right)$. Choose the correct option(s).