A spherically symmetric charge distribution is considered with charge density varying as
$\rho(r)=\left\{\begin{array}{ll}\rho_{0}\left(\frac{3}{4}-\frac{r}{R}\right) & \text { for } r \leq R \\ \text { Zero } & \text { for } r>R\end{array}\right.$
Where, $r ( r < R )$ is the distance from the centre $O$ (as shown in figure). The electric field at point $P$ will be.
A spherically symmetric charge distribution is considered with charge density varying as
$\rho(r)=\left\{\begin{array}{ll}\rho_{0}\left(\frac{3}{4}-\frac{r}{R}\right) & \text { for } r \leq R \\ \text { Zero } & \text { for } r>R\end{array}\right.$
Where, $r ( r < R )$ is the distance from the centre $O$ (as shown in figure). The electric field at point $P$ will be.
- [JEE MAIN 2022]
- A
$\frac{\rho_{0} r}{4 \varepsilon_{0}}\left(\frac{3}{4}-\frac{r}{R}\right)$
- B
$\frac{\rho_{0} r}{3 \varepsilon_{0}}\left(\frac{3}{4}-\frac{r}{R}\right)$
- C
$\frac{\rho_{0} r}{4 \varepsilon_{0}}\left(1-\frac{r}{R}\right)$
- D
$\frac{\rho_{0} r}{5 \varepsilon_{0}}\left(1-\frac{r}{R}\right)$
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List-$I$
List-$II$
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| List-$I$ | List-$II$ |
| $E$ is independent of $d$ | A point charge $Q$ at the origin |
| $E \propto \frac{1}{d}$ | A small dipole with point charges $Q$ at $(0,0, l)$ and $- Q$ at $(0,0,-l)$. Take $2 l \ll d$. |
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| $E \propto \frac{1}{d^3}$ | Two infinite wires carrying uniform linear charge density parallel to the $x$-axis. The one along ( $y=0$, $z =l$ ) has a charge density $+\lambda$ and the one along $( y =0, z =-l)$ has a charge density $-\lambda$. Take $2 l \ll d$ |
| plane with uniform surface charge density |
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