A thin conducting spherical shell of radius R has charge Q spread… - Vidyadip

Question

A thin conducting spherical shell of radius R has charge Q spread uniformly over its surface. Using Gauss’s law, derive an expression for an electric field at a point outside the shell.Draw a graph of electric field E(r) with distance r from the centre of the shell for $0\underline{<}\text{r}\underline{<}\infty.$

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Answer

$\oint\overrightarrow{\text{E}}.\overrightarrow{\text{ds}} = \frac{\text{q}}{\varepsilon_\circ}$$\text{E}\times4\pi\text{r}^{2} =\frac{\text{Q}}{\varepsilon_\circ}$
$\text{E} = \frac{1}{4\pi\varepsilon_\circ}\frac{\text{Q}}{\text{r}^{3}}$

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