A) \[\rho (r)\alpha r\]
B) \[\rho (r)\alpha \frac{1}{{{r}^{2}}}\]
C) \[\rho (r)\alpha \frac{1}{r}\]
D) \[\rho (r)\]= constant
Correct Answer: C
Solution :
[c] |
\[\frac{\Delta V}{\Delta r}\to \] constant |
\[\Rightarrow \] uniform E. field. |
\[(E)\,(4\pi {{r}^{2}})=\frac{1}{{{\varepsilon }_{0}}}\int{\rho dV}\] |
\[(E)\,(4\pi {{r}^{2}})=\frac{1}{{{\varepsilon }_{0}}}\int\limits_{0}^{r}{\rho 4\pi {{r}^{2}}dr}\] |
\[(E)\,(4\pi {{r}^{2}})=\frac{1}{{{\varepsilon }_{0}}}4\pi \int\limits_{0}^{r}{\rho {{r}^{2}}dr}\] |
after integral on RHS |
We must obtain \[{{r}^{2}}\] |
\[\Rightarrow \,\rho \,\propto \frac{1}{r}\] |
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