$A$ hollow conducting sphere of inner radius $R$ and outer radius $2R$ is given a charge $Q$ as shown in the figure. Then,which of the following is true?

$A$ metal cube is given a positive charge $(+Q)$. Which of the following statements is true?

Given below are two statements.
Statement $I$ : Electric potential is constant within and at the surface of each conductor.
Statement $II$ : Electric field just outside a charged conductor is perpendicular to the surface of the conductor at every point.
In the light of the above statements,choose the most appropriate answer from the options given below.

$A$ 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.

Three identical uncharged metal spheres are at the vertices of an equilateral triangle. One at a time,a small sphere is connected by a conducting wire with a large metal sphere that is charged. The center of the large sphere is on the straight line perpendicular to the plane of the equilateral triangle and passing through its center (see figure). As a result,the first small sphere acquires charge $q_1$ and the second acquires charge $q_2$ $(q_2 < q_1)$. The charge that the third sphere $q_3$ will acquire is (Assume $l >> R$,$l >> r$,$d >> R$,$d >> r$):

Two isolated metallic 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 larger sphere is $\sigma_1$. The ratio $\sigma_1$ to $\sigma$ is