Electric Charges and Fields — Physics STD 12 Science — Question

1. Statement: Net electric flux through to a closed surface is equal to $\frac{1}{\varepsilon_\circ}$ times the total net charge enclosed within the surface.

(If the student just writes $\oint\text{E}.\text{ds} =\frac{\text{q}}{\in_\circ}$, award )

2. Diagram:- 

3. Derivation:- 

$\oint\text{E}.\text{ds} \int\limits_{s_1}\overline{E}.\text{d}\overline{s}_{1} + \int\limits_{s_2}\overline{E}.\text{ds}_{2} + \int\limits_{s_3}\overline{E}.\text{ds}_{3}$

$ = 0 + 0 + 2\pi\text{r}\ell$

Also, $\text{q} = \lambda$  $\ell$ (where $\lambda$  is charge per unit length)

$(\text{E}).(2\pi\text{r}\ell) = \frac{1}{\varepsilon_\circ}\lambda\ell $ OR $\text{E}2\pi\text{r}\ell\frac{\text{q}}{\varepsilon_\circ}$

$\text{E} = \frac{\lambda}{2\pi\varepsilon_\circ\text{r}}$ OR $\text{E} = \frac{\text{q}}{2\pi\varepsilon_\circ\text{r}\ell}$.