On a non-conducting ring of radius $R,+q$ and $-q$ charges are uniformly distributed in two halves as shown in figure. The electric field intensity on its axis at a distance $d$ from its centre is given by $\overrightarrow{E}$, then

Two point charges $A$ and $B$ are placed on $X$-axis. Considering electric field $E$ is positive if directed in positive $X$-direction. Variation of electric field strength with distance $x$ is shown in figure for $x$ lying between the charges. Then the nature of charges $A$ and $B$ are respectively

A non-conducting square plate of side length $2a$ is uniformly charged with charge $Q$ and a point charge $q$ is placed at perpendicular distance $a$ as shown in figure. The electric force on the point charge due to plate is

An annular disc of inner radius $R$ and outer radius $2R$ has uniformly distributed charge $Q.$ Electric field strength at point $P$ is

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 ?