C õòjgtkeãnnû õûïïgvtke ejãtég ækõvtkdwvkqp kõ ejãtãevgtkõgæ dû ã ejãtég ægpõkvû jãøkpé vjg hqnnqykpé øãtkãvkqpõ¼ ( ) q t t ³ Ô æ ö r =r – ç ÷ è ø hqt t > Ô r(t) ¿ 0 hqt t ³ Ô Yjgtg t kõ vjg ækõvãpeg htqï vjg egpvtg qh vjg ejãtég ækõvtkdwvkqp rq kõ ã eqpõvãpv. Vjg gngevtke hkgnæ ãv ãp kpvgtpãn òqkpv (t > Ô) kõ¼

Question:

A spherically symmetric charge distribution is characterised by a charge density having the following variations:

$\rho(r)=\rho_{o}\left(1-\frac{r}{R}\right)$ for $r<R$ $\rho(r)=0$ for $r \geq R$

Where $r$ is the distance from the centre of the charge distribution $\rho_{\mathrm{o}}$ is a constant. The electric field at an internal point $(r<R)$ is:

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

  2. $\frac{\rho_{\mathrm{o}}}{\varepsilon_{\mathrm{o}}}\left(\frac{\mathrm{r}}{3}-\frac{\mathrm{r}^{2}}{4 \mathrm{R}}\right)$

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

  4. $\frac{\rho_{0}}{12 \varepsilon_{0}}\left(\frac{r}{3}-\frac{r^{2}}{4 R}\right)$


Correct Option: 2

Solution:

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