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?
$I$
$II$
$III$
$IV$
A non-conducting solid sphere of radius $R$ is uniformly charged. The magnitude of the electric field due to the sphere at a distance $r$ from its centre
Two parallel infinite line charges with linear charge densities $+\lambda\; \mathrm{C} / \mathrm{m}$ and $-\lambda\; \mathrm{C} / \mathrm{m}$ are placed at a distance of $2 \mathrm{R}$ in free space. What is the electric field mid-way between the two line charges?
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
The electric field due to a uniformly charged sphere of radius $R$ as a function of the distance $r$ from its centre is represented graphically by
Consider a sphere of radius $\mathrm{R}$ which carries a uniform charge density $\rho .$ If a sphere of radius $\frac{\mathrm{R}}{2}$ is carved out of it, as shown, the ratio $\frac{\left|\overrightarrow{\mathrm{E}}_{\mathrm{A}}\right|}{\left|\overrightarrow{\mathrm{E}}_{\mathrm{B}}\right|}$ of magnitude of electric field $\overrightarrow{\mathrm{E}}_{\mathrm{A}}$ and $\overrightarrow{\mathrm{E}}_{\mathrm{B}}$ respectively, at points $\mathrm{A}$ and $\mathrm{B}$ due to the remaining portion is