The figure shows a solid metal sphere of radius $a$ surrounded by a concentric thin metal shell of radius $2a$. Initially, both have charges $Q$ each. When the two are connected by a conducting wire as shown in the figure, the amount of heat produced in this process will be:

$A$ hollow conducting sphere is placed in an electric field produced by a point charge placed at $P$ as shown in the figure. Let $V_A, V_B$,and $V_C$ be the potentials at points $A, B$,and $C$ respectively,where $A$ and $B$ are on the surface of the sphere and $C$ is inside the sphere. Then:

$A$ spherical conducting shell of inner radius $r_1$ and outer radius $r_2$ has a charge $Q$.
$(a)$ $A$ charge $q$ is placed at the centre of the shell. What is the surface charge density on the inner and outer surfaces of the shell?
$(b)$ Is the electric field inside a cavity (with no charge) zero,even if the shell is not spherical,but has any irregular shape? Explain.

Consider three concentric metallic spheres $A, B$ and $C$ of radii $a, b, c$ respectively,where $a < b < c$. $A$ and $B$ are connected,whereas $C$ is grounded. The potential of the middle sphere $B$ is raised to $V$. Then the charge on the sphere $C$ is

By keeping a conductor in an external electric field and from the results obtained by electrostatics,which of the following options is wrong?

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 ........