A spherically symmetric charge distribution is characterised by a charge density having the following variations

$\rho (r)\, = \,{\rho _0}\left( {1 – \frac{r}{R}} \right)$ for $r < R$

$\rho (r)\,=\,0$ for $r\, \ge \,R$

Where $r$ is the distance from the centre of the charge distribution $\rho _0$ is a constant. The electric field at an internal point $(r < R)$ is

Consider a uniform spherical volume charge distribution of radius $R$. Which of the following graphs correctly represents the magnitude of the electric field $E$ at a distance $r$ from the centre of the sphere?

Consider a uniform spherical charge distribution of radius $R_1$ centred at the origin $O$. In this distribution, a spherical cavity of radius $R_2$, centred at $P$ with distance $O P=a=R_1-R_2$ (see figure) is made. If the electric field inside the cavity at position $\overrightarrow{ r }$ is $\overrightarrow{ E }(\overrightarrow{ r })$, then the correct statement$(s)$ is(are) $Image$

At a point $20\, cm$ from the centre of a uniformly charged dielectric sphere of radius $10\, cm$, the electric field is $100\, V/m$. The electric field at $3\, cm$ from the centre of the sphere will be…….$V/m$

A solid ball of radius $R$ has a charge density $\rho $ given by $\rho  = {\rho _0}\left( {1 – \frac{r}{R}} \right)$ for $0 \leq r \leq R$. The electric field outside the ball is