Consider the shown system of two concentric thin metal shells. The inner hell has charge $Q$, while the outer shell is neutral. Potential difference between the shells is $V$. If the shell are joined by metal wire, then potential of the inner shell is

$(a)$ A conductor $A$ with a cavity as shown in Figure $(a)$ is given a charge $Q$. Show that the entire charge must appear on the outer surface of the conductor.

$(b)$ Another conductor $B$ with charge $q$ is inserted into the cavity keeping $B$ insulated from $A$. Show that the total charge on the outside surface of $A \text { is } Q+q$ [Figure $(b)$]

$(c)\;A$ sensitive instrument is to be shielded from the strong electrostatic fields in its environment. Suggest a possible way.

Consider an initially neutral hollow conducting spherical shell with inner radius $r$ and outer radius $2 r$. A point charge $+Q$ is now placed inside the shell at a distance $r / 2$ from the centre. The shell is then grounded by connecting the outer surface to the earth. $P$ is an external point at a distance $2 r$ from the point charge $+Q$ on the line passing through the centre and the point charge $+Q$ as shown in the figure. The magnitude of the force on a test charge $+q$ placed at $P$ will be

Inside a hollow charged spherical conductor, the potential

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)

Figure shows a solid conducting sphere of radius $1 m$, enclosed by a metallic shell of radius $3 \,m$ such that their centres coincide. If outer shell is given a charge of $6 \,\mu C$ and inner sphere is earthed, find magnitude charge on the surface of inner shell is ............. $\mu C$