A small electric dipole of dipole moment $p$ is placed perpendicular to an infinitely long wire of linear charge density $\lambda .$ The centre of dipole is at a distance $r$ from the wire as shown. The electric force on the dipole is

A dielectric slab is placed in uniform electric field $E$ as shown in figure. Then

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?