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← JEE Main 2014 · 12 Apr · Shift 1
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JEE Main 2014 · 12 Apr · Shift 1, Physics question 16

A spherically symmetric charge distribution is characterised by a charge density having the following variation :
ρ(r)=ρo(1−rR) for r<R,ρ(r)=0 for r≥R\rho(r)=\rho_o\left(1-\frac rR\right)\ \text{for } r<R,\qquad\rho(r)=0\ \text{for } r\ge R
Where r is the distance from the centre of the charge distribution and ρo\rho_o is a constant. The electric field at an internal point (r < R) is :

Choose one option
Answer and worked solution

Official answer: B

Enclosed charge:
q(r)=∫0r4πr′2ρo(1−r′R)dr′=4πρo(r33−r44R).q(r)=\int_0^r4\pi r'^2\rho_o\left(1-\frac{r'}R\right)dr'=4\pi\rho_o\left(\frac{r^3}3-\frac{r^4}{4R}\right).
E=q4πϵor2=ρoϵo(r3−r24R).E=\frac{q}{4\pi\epsilon_or^2}=\frac{\rho_o}{\epsilon_o}\left(\frac r3-\frac{r^2}{4R}\right).

Topics:Electric flux and Gauss's law
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