The total charge enclosed in an incremental volume of 2 × 10 - 9 m3… | JEE Main 2021 (22 Jul, Shift 2)

Q86JEE Main 2021 · 22 JUL · SHIFT 2Medium

Electric Flux & Gauss's Law

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 $\hat{i} -$ e $-$ x cos y $\hat{j}$ + 2z $\hat{k}$ C/m2

Numerical answer type. Work it out, then open the answer.

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Answer: 4

Gauss's law in point form: $\rho = \nabla\cdot\vec D$ .
$\nabla\cdot\vec D = -e^{-x}\sin y + e^{-x}\sin y + 2 = 2$ C/m $^3$
$Q = \rho V = 2\times2\times10^{-9} = 4\times10^{-9}$ C $= 4$ nC.

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