Some charge is being given to a conductor. Then its potential is

$A$ metallic spherical shell has an inner radius $R_1$ and an outer radius $R_2$. $A$ charge $Q$ is placed at the center of the spherical cavity. What will be the surface charge density on $(i)$ the inner surface,and $(ii)$ the outer surface?

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 spheres of radius $a$ and $b$ respectively are charged and joined by a wire. The ratio of the electric field at the surfaces of the spheres is

Two concentric spherical shells of radius $R_1$ and $R_2$ have $q_1$ and $q_2$ charge respectively as shown in the figure. How much charge will flow through key $k$ when it is closed?

Two charged conducting spheres of radii $a$ and $b$ are connected to each other by a wire. What is the ratio of electric fields at the surfaces of the two spheres? Use the result obtained to explain why charge density on the sharp and pointed ends of a conductor is higher than on its flatter portions.