Question 140 of 311

Let $P(r)=\frac{Q}{\pi R^4} r$ be the charge density distribution for a solid sphere of radius $R$ and total charge $Q$. for a point ' $p$ ' inside the sphere at distance $r_1$ from the centre of the sphere, the magnitude of electric field is

A0B$\frac{Q}{4 \pi \varepsilon_0 r_1^2}$C$\frac{Q r_1^2}{4 \pi \varepsilon_0 R^4}$D$\frac{Q_1^2}{3 \pi \varepsilon_0 R^4}$

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Answer: (C) $\frac{Q r_1^2}{4 \pi \varepsilon_0 R^4}$

$$E 4 \pi r_1^2=\frac{\int_0^{r_1} \frac{Q}{\pi R^4} r 4 \pi r^2 d r}{\varepsilon_0} \Rightarrow E=\frac{Q r_1^2}{4 \pi \varepsilon_0 R^4} .$$