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

$A$ dipole consisting of two charges $\pm q$ separated by a distance $2a$ is placed with its centre at a distance $D$ from the center of a grounded conducting sphere of radius $R$ $(D \gg a)$. When the dipole moment vector is perpendicular to the line joining the two centres (those of the dipole and sphere),the total charge induced on the sphere is:

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?

Two 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 $A$

Consider two concentric spherical metal shells of radii $r_{1}$ and $r_{2}$ $(r_{2} > r_{1})$. If the outer shell has a charge $q$ and the inner one is grounded,the charge on the inner shell is

Charge on the outer sphere is $q$ and the inner sphere is grounded. The charge on the inner sphere is $q'$,for $(r_2 > r_1)$. Then