The figure shows three concentric metallic spherical shells. The outermost shell has charge $q_2$,the innermost shell has charge $q_1$,and the middle shell is uncharged. The charge appearing on the inner surface of the outermost shell is

$A$ sphere '$1$' with radius $R$ has charge $q$. Sphere '$2$' with radius $3R$ is far from sphere '$1$' and is initially uncharged. If the two spheres are now connected with a thin conducting wire,then the ratio $\frac{\sigma_1}{\sigma_2}$ of the surface charge densities is

$A$ solid conducting sphere of radius $a$ has a net positive charge $2Q$. $A$ conducting spherical shell of inner radius $b$ and outer radius $c$ is concentric with the solid sphere and has a net charge $-Q$. The surface charge density on the inner and outer surfaces of the spherical shell will be

Two spherical conductors $A$ and $B$ of radii $1 \ mm$ and $2 \ mm$ are separated by a distance of $5 \ cm$ and are uniformly charged. If the spheres are connected by a conducting wire,then in the equilibrium condition,the ratio of the magnitude of the electric fields at the surfaces of spheres $A$ and $B$ is:

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:

Consider two concentric spherical metal shells of radii $r_{1}$ and $r_{2}$ $(r_{2} > r_{1})$. If the outer shell has a charge $q$ and the inner one is grounded, the charge on the inner shell is