According to Gauss’ Theorem, electric field of an infinitely long straight wire is proportional to

In the figure, a very large plane sheet of positive charge is shown. $P _{1}$ and $P _{2}$ are two points at distance $l$ and $2 \,l$ from the charge distribution. If $\sigma$ is the surface charge density, then the magnitude of electric fields $E_{1}$ and $E_{2}$ at $P _{1}$ and $P _{2}$ respectively are

Which of the following graphs shows the variation of electric field $E$ due to a hollow spherical conductor of radius $R$ as a function of distance $r$ from the centre of the sphere

An isolated sphere of radius $R$ contains uniform volume distribution of positive charge. Which of the curve shown below, correctly illustrates the dependence of the magnitude of the electric field of the sphere as a function of the distance $r$ from its centre?

An infinitely long solid cylinder of radius $R$ has a uniform volume charge density $\rho $. It has a spherical cavity of radius $R/2$ with its centre on the axis of the cylinder, as shown in the figure. The magnitude of the electric field at the point $P$, which is at a distance $2R$ from the axis of the cylinder, is given by the expression $\frac{{23\rho R}}{{16K{\varepsilon _0}}}$ .The value of $K$ is

Let there be a spherically symmetric charge distribution with charge density varying as $\rho (r)=\;\rho _0\left( {\frac{5}{4} - \frac{r}{R}} \right)$, upto $r = R$ ,and $\rho (r) = 0$ for $r > R$ , where $r$ is the distance from the origin. The electric field at a distance $r(r < R)$ from the origin is given by