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

For a spherical shell,which of the following statements is correct?

$A$ 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:
$(A)$ $E_A^{\text{inside}} = 0$
$(B)$ $Q_A > Q_B$
$(C)$ $\frac{\sigma_A}{\sigma_B} = \frac{R_B}{R_A}$
$(D)$ $E_A^{\text{on surface}} < E_B^{\text{on surface}}$

Two metal spheres of radius $R$ and $3R$ have the same surface charge density $\sigma$. If they are brought in contact and then separated,the surface charge density on the smaller and bigger sphere becomes $\sigma_1$ and $\sigma_2$,respectively. The ratio $\frac{\sigma_1}{\sigma_2}$ is:

Two charged conducting spheres $S_1$ and $S_2$ of radii $8 \text{ cm}$ and $18 \text{ cm}$ are connected to each other by a wire. After equilibrium is established, the ratio of electric fields on $S_1$ and $S_2$ spheres are $E_{S_1}$ and $E_{S_2}$ respectively. The value of $\frac{E_{S_1}}{E_{S_2}}$ is . . . . . . .