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  • The electric field inside a sphere which carries a volume charge density proportional to the distance from the origin  <img alt="\rho=ar" src="https://entrancecorner.oncodecogs.com/gif.latex?%

The electric field inside a sphere which carries a volume charge density proportional to the distance from the origin  \rho=ar (a is a constant) is :

Option: 1

\frac{\alpha\; r^{3}}{4\; \epsilon _{0}}         


Option: 2

\frac{\alpha\; r^{2}}{4\; \epsilon _{0}}


Option: 3

\frac{\alpha\; r^{2}}{3\; \epsilon _{0}}


Option: 4

none of these


Answers (1)

best_answer

Consider an elementary shell of radius x and thickness dx.      

                                

E=\frac{k\int dq}{r^{2}}=\frac{k\int_{0}^{r}4\pi x^{2}dx\left ( a x \right )}{r^{2}}

=\frac{k4\pi a }{r^{2}}\int_{0}^{r}x^{3}dx=\frac{a r^{2}}{4\varepsilon _{0}}

Posted by

Ritika Jonwal

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