A hemisphere of radius $R$ as shown in figure is uniformly charged with a surface charge density $\sigma .$ The electric field at the centre $C$ is

Two non-conducting infinitely long straight wires with uniform linear charge densities ${\lambda }_1$ and ${\lambda }_2$ are arranged along $X$ and $Y$-axis respectively. Their point of intersection is at origin. One of the field lines due to these wires in $X-Y$ plane is a straight line passing through the origin. The angle made by this line with $X$-axis is

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)