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

$12 \mu C$ and $6 \mu C$ charges are given to two conducting plates having the same cross-sectional area and placed face to face close to each other as shown in the figure. The resulting charge distribution in $\mu C$ on surfaces $A, B, C$ and $D$ are respectively,

Two metallic concentric shells are shown. Before closing the switch,the charge on the inner shell is $Q$ and the charge on the outer shell is $2Q$. The potential at point $A$ is $V$. What will be the potential at the same point after closing the switch?

The charge given to any conductor resides on its outer surface,because

$A$ solid spherical conducting shell has an inner radius $a$ and an outer radius $2a$. At the center of the shell is located a point charge $+Q$. What must the excess charge of the shell be in order for the charge density on the inner and outer surfaces of the shell to be exactly equal?

Five identical conducting plates,each of face area $A$,are placed parallel to each other with a separation of $d$ between two adjacent plates as shown in the figure. The plates $M$ and $N$ are given charges $Q_1$ and $Q_2$ respectively and the remaining plates are neutral. If the outermost plates are grounded,the potential difference between the plates $M$ and $N$ is . . . . . .