An electrostatic field in a region is radially outward with magnitude $E$ = $\alpha r$ , where $\alpha $ is a constant and $r$ is radial distance. The charge contained in a sphere of radius $R$ in this region (centred at the origin) is

Obtain the expression of electric field by charged spherical shell on a point outside it.

Consider an atom with atomic number $Z$ as consisting of a positive point charge at the centre and surrounded by a distribution of negative electricity uniformly distributed within a sphere of radius $R$. The electric field at a point inside the atom at a distance $r$ from the centre is

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

A spherical conductor of radius $12 \;cm$ has a charge of $1.6 \times 10^{-7} \;C$ distributed uniformly on its surface. What is the electric field

$(a)$ inside the sphere

$(b)$ just outside the sphere

$(c)$ at a point $18\; cm$ from the centre of the sphere?

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