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
$\frac{ Ze }{4 \pi \varepsilon_0}\left[\frac{1}{r^2}-\frac{r}{R^3}\right]$
$\frac{Z e}{4 \pi \varepsilon_0}\left[\frac{1}{r^2}+\frac{1}{R^3}\right]$
$\frac{2 Z e}{4 \pi \varepsilon_0 r^2}$
$0$
The electric field at a distance $r$ from the centre in the space between two concentric metallic spherical shells of radii $r_1$ and $r_2$ carrying charge $Q_1$ and $Q_2$ is $(r_1 < r < r_2)$
Obtain the expression of electric field by ......
$(i)$ infinite size and with uniform charge distribution.
$(ii)$ thin spherical shell with uniform charge distribution at a point outside it.
$(iii)$ thin spherical shell with uniform charge distribution at a point inside it.
The volume charge density of a sphere of radius $6 \,m$ is $2 \,\mu cm ^{-3}$. The number of lines of force per unit surface area coming out from the surface of the sphere is $....\times 10^{10}\, NC ^{-1}$. [Given : Permittivity of vacuum $\left.\epsilon_{0}=8.85 \times 10^{-12} C ^{2} N ^{-1}- m ^{-2}\right]$
Obtain the expression of electric field by a straight wire of infinite length and with linear charge density $'\lambda '$.
A solid metallic sphere has a charge $ + \,3Q$. Concentric with this sphere is a conducting spherical shell having charge $ - Q$. The radius of the sphere is $a$ and that of the spherical shell is $b(b > a)$. What is the electric field at a distance $R(a < R < b)$ from the centre