Let there be a spherically symmetric charge distribution with charge… | JEE Main 2010 (AIEEE)

Q123JEE Main 2010 · AIEEEDifficult

Electric Flux & Gauss's Law

Let there be a spherically symmetric charge distribution with charge density varying as $\rho(r) = \rho_0\left(\frac{5}{4} - \frac{r}{R}\right)$ upto $r = R,$ and $\rho(r) = 0$ for $r > R,$ where $r$ is the distance from the origin. The electric field at a distance $r\ (r < R)$ from the origin is given by

Show answer and solution

Answer: (a)

Enclosed charge: $q = 4\pi\rho_0\int_0^r\left(\frac{5}{4}r^2 - \frac{r^3}{R}\right)dr = 4\pi\rho_0\left(\frac{5r^3}{12} - \frac{r^4}{4R}\right) = \pi\rho_0 r^3\left(\frac{5}{3} - \frac{r}{R}\right)$
$E = \frac{q}{4\pi\varepsilon_0 r^2} = \frac{\rho_0 r}{4\varepsilon_0}\left(\frac{5}{3} - \frac{r}{R}\right)$
So the answer is (a).

Report a mistake

More questions on Electric Flux & Gauss's Law

Let ρ(r) = Qπ R⁴r be the charge density distribution for a solid sphere of radius R and…JEE Main 2009 (AIEEE)
A thin spherical shell of radius R has charge Q spread uniformly over its surface. Which…JEE Main 2008 (AIEEE)
A hollow cylinder has a charge q coulomb within it. If φ is the electric flux in units of…NEET 2007 (AIPMT)
A square surface of side L metres is in the plane of the paper. A uniform electric field…NEET 2006 (AIPMT)
A charge q is located at the centre of a cube. The electric flux through any face isNEET 2003 (AIPMT)
If the electric flux entering and leaving an enclosed surface respectively is φ₁ and φ₂…JEE Main 2003 (AIEEE)
A charged particle q is placed at the centre O of cube of length L(ABCDEFGH). Another…JEE Main 2002 (AIEEE)
A charge Q μ C is placed at the centre of a cube, the flux coming out from each face will…NEET 2001 (AIPMT)

Electric Flux & Gauss's Law question from JEE Main 2010 (AIEEE)

More questions on Electric Flux & Gauss's Law