Question
State Gauss's theorem in electrostatics. Apply this theorem to derive an expression for electric field intensity at a point near an infinitely long straight charged wire.
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Answer
- 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.
- Diagram:-
- Derivation:-
$ = 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 $\text{E} = \frac{\text{q}}{2\pi\varepsilon_\circ\text{r}\ell}$.
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