Q 12-01-098JEE MainJEE Main 2022 (25 Jul, Shift 1)Medium
The volume charge density of a sphere of radius $6\ \text{m}$ is $2\ \mu\text{C cm}^{-3}$. The number of lines of force per unit surface area coming out from the surface of the sphere is ______ $\times10^{10}\ \text{N C}^{-1}$. [Given: permittivity of vacuum $\varepsilon_0 = 8.85\times10^{-12}\ \text{C}^2\text{N}^{-1}\text{m}^{-2}$]
Numerical value type. Enter your answer.
Answer: 45
Lines per unit area equal the field at the surface. $\rho = 2\ \mu\text{C cm}^{-3} = 2\ \text{C m}^{-3}$.
$$E = \frac{\rho R}{3\varepsilon_0} = \frac{2\times6}{3\times8.85\times10^{-12}}\approx4.5\times10^{11} = 45\times10^{10}\ \text{N C}^{-1}$$
Solution by Sreeraj P, M.Sc Physics