A ring of radius $R$ is uniformly charged. Linear charge density is $\mathrm{\lambda }$. An imaginary sphere of radius $R$ is drawn with its centre on circumference of ring. Total electric flux passing through the sphere would be

A ring of radius $R$ is placed at a distance $R$ from a point charge $q$ as shown in figure. Total electric flux passing through the ring would be

A point charge $q$ is placed at a distance $r$ from the centre $O$ of an uncharged spherical shell of inner radius $R$ and outer radius $2R.$ The distance is $r<R.$ The electric potential at the centre of the shell will be

A hollow sphere of radius $r$ is put inside another hollow sphere of radius $R$. The charges on the two are $+Q$ and $-q$ as shown in the figure. A point $P$ is located at a distance $x$ from the common centre such that $r<x<R$. The potential at the point $P$ is

The curve represents the distribution of potential along the straight line joining the two charges $Q_1$ and $Q_2$ (separated by a distance $r$$)$, then which is of the following statements are correct?

$1.$ $\left|Q_1\right|>\left|Q_2\right|$

$2.$ $Q_1$ is positive in nature

$3.$ $A$ and $B$ are equilibrium points

$4.$ $C$ is a point of unstable equilibrium

Which of the above statements are correct?

A solid conducting sphere of radius $a$ having a charge $q$ is surrounded by a concentric conducting spherical shell of inner radius $2a$ and outer radius $3a$ as shown in figure. Find the amount of heat produced when switch is closed.

$k=\frac{1}{4{\mathrm{\pi \epsilon }}_0}$

Figure shows two conducting thin concentric shells of radii $r$ and $3r$. The outer shell carries charge $q$. Inner shell is neutral. Find the charge that will flow from inner shell to earth after the switch $S$ is closed.