The magnitude of electric field on the surface of a uniformly charged metalic spherical shell is $E$. If a hole is made in it using a insulating device, then the magnitude of electric field in the hole will be

A hollow closed conductor of irregular shape is given some charge. Which of the following statements are correct ?

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 $A$

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 ............. $\mu C$

$(a)$ 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.

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