Consider an isolated, thin conducting spherical shell $A$ of radius $20 \mathrm{cm}$. The shell is given a charge $Q_A$ that distributes uniformly and due to $Q_A$ only the maximum strength of the resulting electric field has a value $11250 \mathrm{N} {\mathrm{C}}^{-1}$ due to $Q_A$ only. $B$ is another isolated thin conducting spherical shell of radius $40 \mathrm{cm}$. It is given a charge $Q_B$ that distributes uniformly and in this case, maximum strength of the resulting field has a value $4500 \mathrm{N} {\mathrm{C}}^{-1}$ due to $Q_B$ only. The two shells $A$ and $B$ are now kept in a concentric manner as shown in figure. $x,y$ and $z$ are points as shown in figure, at distance $10 \mathrm{cm}, 30 \mathrm{cm}, 50 \mathrm{cm}$ from the centre, respectively. [Take $V=0$ at $r=\infty$]

Using Gauss law, derive expression for electric field due to a spherical shell of uniform charge distribution $\sigma$ and radius $R$ at a point lying at a distance $x$ from the centre of shell, such that $x>R$.

A solid metal sphere of radius $R$ having charge $q$ is enclosed inside the concentric spherical shell of inner radius $a$ and outer radius $b$ as shown in the figure. The approximate variation of electric field $\overrightarrow{E}$, as a function of distance $r$, from centre $O$, is given by:

Using Gauss law, derive expression for electric field due to a spherical shell of uniform charge distribution $\sigma$ and radius $R$ at a point lying at a distance $x$ from the centre of shell, such that $0<x<R$.

Electric intensity outside a charged cylinder having the charge per unit length $\lambda$ at a distance $r$ from its axis is ____.

Two non-conducting spheres of radii $R_1$ and $R_2$ and carrying uniform volume charge densities $+\rho$ and $-\rho$, respectively, are placed such that they partially overlap, as shown in the figure. At all points in the overlapping region,

State Gauss's law in electrostatics and write in its mathematical form.Calculate the electric field $\overrightarrow{\mathrm{E}}$ at point $\mathrm{P}$ due to charges this spherical shell, shown in figure (1) What will be the field $\overrightarrow{E}$ shown in fig (2) and (3)? Given the surface charge density is $\sigma$.