Two spherical conductors $A$ and $B$ of radii $1\, mm$ and $2\, mm$ are placed at a distance of $5\, cm$ from each other. They carry equal charges. If the spheres are connected by a conducting wire,they reach an equilibrium state. The ratio of the magnitudes of the electric fields at the surfaces of spheres $A$ and $B$ is ........

Under electrostatic condition of a charged conductor,which among the following statements is true?

$(a)$ $A$ 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 $A$ 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.

$A$ 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

Which of the following statements is always true for a charged conductor?
$(1)$ The electric field just outside the surface is parallel to the surface.
$(2)$ $E_{in} = 0$
$(3)$ Electric field lines are perpendicular to the equipotential surface.

Two conducting spheres of radii $20\, cm$ and $15\, cm$ are placed on insulating stands. Both are given an equal charge of $10\ \mu C$. When they are connected by a copper wire and then disconnected,which of the following is true?