Let there be a spherically symmetric charge distribution with charge density varying as

Question:

Let there be a spherically symmetric charge distribution with charge density varying as $\rho(r)=\rho_{0}\left(\frac{5}{4}-\frac{r}{R}\right)$ upto $r=R$, and $\rho(r)=0$ for $r>R$, where $r$ is the distance from the origin. The electric field at a distance $r(r

 

  1. $\frac{\rho_{0} \mathrm{r}}{3 \varepsilon_{0}}\left(\frac{5}{4}-\frac{\mathrm{r}}{\mathrm{R}}\right)$

  2. $\frac{4 \pi \rho_{0} r}{3 \varepsilon_{0}}\left(\frac{5}{3}-\frac{r}{R}\right)$

  3. $\frac{\rho_{0} r}{4 \varepsilon_{0}}\left(\frac{5}{3}-\frac{r}{R}\right)$

  4. $\frac{4 \rho_{0} r}{3 \varepsilon_{0}}\left(\frac{5}{4}-\frac{r}{R}\right)$

Correct Option: , 3

Solution:

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