The intensity of the electric field at a charged point inside a hollow metallic container is ....... .

$A$ spherical metal shell $A$ of radius $R_A$ and a solid metal sphere $B$ of radius $R_B < R_A$ are kept far apart and each is given charge $+Q$. Now they are connected by a thin metal wire. Then:
$(A)$ $E_A^{\text{inside}} = 0$
$(B)$ $Q_A > Q_B$
$(C)$ $\frac{\sigma_A}{\sigma_B} = \frac{R_B}{R_A}$
$(D)$ $E_A^{\text{on surface}} < E_B^{\text{on surface}}$

Consider two conducting spheres of radii $R_1$ and $R_2$ with $(R_1 > R_2)$. If the two are at the same potential,the larger sphere has more charge than the smaller sphere. State whether the charge density of the smaller sphere is more or less than that of the larger one.

Two isolated metallic solid spheres of radii $R$ and $2R$ are charged such that both have the same charge density $\sigma$. The spheres are then connected by a thin conducting wire. If the new charge density of the bigger sphere is $\sigma^{\prime}$,then the ratio $\frac{\sigma^{\prime}}{\sigma}$ is:

$A$ 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.

$A$ hollow closed conductor of irregular shape is given some charge. Which of the following statements are correct?