Let $P\left( r \right) = \frac{Q}{{\pi {R^4}}}r$ 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

  • A

    zero

  • B

    $\frac{Q}{{4\pi {\varepsilon _0}r_1^2}}$

  • C

    $\frac{{Qr_1^2}}{{4\pi {\varepsilon _0}{R^4}}}$

  • D

    $\frac{{Qr_1^2}}{{3\pi {\varepsilon _0}{R^4}}}$

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  • [JEE MAIN 2024]

Mention applications of Gauss’s law.

Electric field at a point varies as ${r^o}$ for