Question

The volume charge density of a sphere of radius $6m$ is $2\mu C{m}^{-3}$. The number of lines of force per unit surface area coming out from the surface of the sphere is ________$\times$ $10^{10}N{C}^{-1}$.
[Given : Permittivity of vacuum
${ϵ}_0=8.85\times 10^{-12}{C}^2{N}^{-1}-m^{-2}]$

Answer 1

Answer: 45

No. of electric field lines per unit area $=$ electric field.
$E=\frac{\rho r}{3{\in }_0}$, for $r=R$
$E=\frac{\rho R}{3{ϵ}_0}=\frac{2\times 6}{3\times 8.85\times 10^{-12}}=0.45\times 10^{12}N{C}^{-1}$
$=45\times 10^{10}N/C$