A spherically symmetric charge distribution is characterised by a charge density having…

Physics · JEE Main · NTA Exams — Electrostatics

A spherically symmetric charge distribution is characterised by a charge density having the following variation:
\(\rho(r)=\rho_{0}\left(1-\frac{r}{R}\right) \text { for } r\(\rho(\mathrm{r})=0\) for r > R
Where r is the distance from the centre of the charge distribution and ρO is a constant. The electric field at an internal point (r < R) is:
  1. \(\frac{\rho_{\mathrm{o}}}{3 \epsilon_{\mathrm{o}}}\left(\frac{\mathrm{I}}{3}-\frac{\mathrm{r}^{2}}{4 \mathrm{R}}\right)\)
  2. \(\frac{\rho_{o}}{4 \epsilon_{o}}\left(\frac{r}{3}-\frac{r^{2}}{4 R}\right)\)
  3. \(\frac{\rho_{o}}{\epsilon_{o}}\left(\frac{\mathrm{r}}{3}-\frac{\mathrm{r}^{2}}{4 \mathrm{R}}\right)\)
  4. \(\frac{\rho_{o}}{12 \epsilon_{o}}\left(\frac{\mathrm{I}}{3}-\frac{\mathrm{r}^{2}}{4 \mathrm{R}}\right)\)

Answer

(C) _ o _ o ( r 3 - r ^ 2 4 R )

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