For a thin spherical shell of radius $R$ with a uniform surface charge density, which of the following graphs best represents the variation of the electric field magnitude $|\vec{E}(r)|$ and the electric potential $V(r)$ with the distance $r$ from the center?

$A$ circular ring carries a uniformly distributed positive charge. The electric field $(E)$ and potential $(V)$ vary with distance $(r)$ from the centre of the ring along its axis as:

An empty thick conducting shell of inner radius $a$ and outer radius $b$ is shown in the figure. It is observed that the inner face of the shell carries a uniform charge density $-\sigma$ and the outer surface carries a uniform charge density $+\sigma'$. If a point charge $q_A$ is slowly moved inside the cavity of the shell,then choose the correct statement$(s)$.

Two point charges of $40 \ \mu C$ and $-20 \ \mu C$ are placed at a certain distance. If they are brought into contact and then placed at the same distance,what is the ratio of the electrostatic force in the two cases?

Two equal negative charges are fixed at the points $(0, a)$ and $(0, -a)$ on the $y$-axis. $A$ positive charge $Q$ is released from rest at the point $(2a, 0)$ on the $x$-axis. The charge $Q$ will

Two identical charged spheres of material density $\rho$,suspended from the same point by inextensible strings of equal length,make an angle $\theta$ between the strings. When suspended in a liquid of density $\sigma$,the angle $\theta$ remains the same. The dielectric constant $K$ of the liquid is