A thin conducting spherical shell (center at $O$ ) having charge $Q_0$ , radius $R$ and three point charges $Q_0$ , $-2Q_0$ , $3Q_0$ are also kept at point $A$ , $B$ and $C$ respectively as shown. Find the potential at any point on the conducting shell. (Potential at infinity is assumed to be zero)

An empty thick conducting shell of inner radius $a$ and outer radius $b$ is shown in figure.If it is observed that the inner face of the shell carries a uniform charge density $-\sigma$ and the surface carries a uniform charge density $ '\sigma '$

If another point charge $q_B$ is also placed at a distance $c ( > b) $ the center of shell, then choose the correct statements 

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

A positive point charge $q$ is placed at a distance $2 R$ from the surface of a metallic shell of radius $R$. The electric field at centre of shell due to induced charge has magnitude

Two concentric spheres $A$ and $B$ are kept very near to each other. $A$ is negatively charged and $B$ is earthed. The true statement is

$(A)$ Charge on $B$ is zero

$(B)$ Potential at $B$ is zero

$(C)$ Charge is uniformly distributed on $A$

$(D)$ Charge is non uniformly distributed on $A$

A hollow metal sphere of radius $5\,\, cm$ is charged so that the potential on its surface is $10\,\, V$. The potential at the centre of the sphere is.....$V$