Medium INTEGER +4 / -1 PYQ · JEE Mains 2021

The total charge enclosed in an incremental volume of 2 $\times$ 10$-$9 m3 located at the origin is ___________ nC, if electric flux density of its field is found as

D = e$-$x sin y $\widehat i$ $-$ e$-$x cos y $\widehat j$ + 2z $\widehat k$ C/m2

Answer (integer) 4

Solution

$\overline D = {\varepsilon _0}\overline E$<br><br>$Div.\,\overline E = {\rho \over {{\varepsilon _0}}}$<br><br>$\Rightarrow div.\,\overline D = \rho$<br><br>$$ \Rightarrow {\partial \over {\partial x}}\left( {{e^{ - x}}\sin y} \right) + {\partial \over {\partial y}}\left( { - {e^{ - x}}\cos y} \right) + {\partial \over {\partial z}}(2z) = \rho $$<br><br>$\Rightarrow$ $\rho$ = 2 (a constant)<br><br>V = 2 $\times$ 10<sup>$-$9</sup> m<sup>3</sup><br><br>q = 2 $\times$ 2 $\times$ 10<sup>$-$9</sup> = 4 nC

About this question

Subject: Physics · Chapter: Electrostatics · Topic: Coulomb's Law

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