Find the electric field intensity due to a uniformly charged spherical shell at a point (i) outside the shell and (ii) inside the shell. Plot the graph of electric field with distance from the centre of the shell.
CBSE OUTSIDE DELHI - SET 3 NORTH 2016
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We have by Gauss’s law $\oint\overrightarrow{\text{E}}.\overrightarrow{\text{ds}} = \frac{\text{Q}_{eclosed}}{\in_{0}}$Let Q be the total charge on the shell.
$\text{E}.4\pi\text{r}^{2} = \frac{\text{Q}}{\in_{0}}$
$\therefore\text{E} = \frac{1}{4\pi\in_{0}}\frac{\text{Q}}{\text{r}^{2}}$
$\therefore\text{E} = 0 $
The graph is as shown
- For the point M outside the shell, we have
$\text{E}.4\pi\text{r}^{2} = \frac{\text{Q}}{\in_{0}}$
$\therefore\text{E} = \frac{1}{4\pi\in_{0}}\frac{\text{Q}}{\text{r}^{2}}$
- For the point N inside the shell, as charge enclosed inside the shell is zero.
$\therefore\text{E} = 0 $
The graph is as shown
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