An insulated sphere with dielectric constant $K$ (where $K>1$) of radius of $R$ is having a total charge $+Q_0$ uniformly distributed in the volume. It is kept inside a metallic sphere of inner radius $2R$ and outer radius $3R$. Whole system is kept inside a metallic shell of radius $4R$, metallic sphere is earthed as shown in the figure. Spherical shell of radius $4R$ is given a charge $+Q_0$. Consider $E-r$ graph for $r>0$ only. Where $E$ and $r$ represents electric field and radial distance from the centre respectively. Then choose the CORRECT option(s)

 

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,

Let $\sigma$ be the uniform surface charge density of two infinite thin plane sheets shown in figure. Then the electric fields in three different region $E_I , E_{II}$ and $E_{III}$

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:

As shown in the figure, a point charge $Q$ is placed at the centre of conducting spherical shell of inner radius $a$ and outer radius $b$. The electric field due to charge $Q$ in three different regions $I, II \text{and} III$ is given by : $(I : r < a, II : a < r < b, III : r > b)$

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

A spherically symmetric charge distribution is considered with charge density varying as

$\rho \left(r\right)=\left\{\begin{array}{ll}{\rho }_0\left(\frac{3}{4}-\frac{r}{R}\right)& \text{ for }r\le R\\ \mathrm{Zero}& & & \mathrm{for} r>R\end{array}\right.$

Where, $r\left(r<R\right)$ is the distance from the centre $O$ (as shown in figure). The electric field at point $P$ will be :