Figure shows a charged conductor resting on an insulating stand. If at the point $P$ the charge density is $\sigma $, the potential is $V$ and the electric field strength is $E$, what are the values of these quantities at point $Q$

Charge density        potential        Electric intensity

The dielectric strength of air at $NTP$ is $3 \times {10^6}\,V/m$ then the maximum charge that can be given to a spherical conductor of radius $3\, m$ is

For the situation shown in the figure below, mark out the correct statement

A thin conducting spherical shell (center at $O$ ) having charge $Q_0$ , radius $R$ and three point charges $Q_0$ , $-2Q_0$ , $3Q_0$ are also kept at point $A$ , $B$ and $C$ respectively as shown. Find the potential at any point on the conducting shell. (Potential at infinity is assumed to be zero)

A spherical conducting shell of inner radius $r_1$ and outer radius $r_2$ has a charge $Q. $

$(a)$ A charge $q$ is placed at the centre of the shell. What is the surface charge density on the inner and outer surfaces of the shell?

$(b)$ Is the electric field inside a cavity (with no charge) zero, even if the shell is not spherical, but has any irregular shape? Explain.

An empty thick conducting shell of inner radius $a$ and outer radius $b$ is shown in figure.If it is observed that the inner face of the shell carries a uniform charge density $-\sigma$ and the surface carries a uniform charge density $ '\sigma '$

If another point charge $q_B$ is also placed at a distance $c ( > b) $ the center of shell, then choose the correct statements