The total charge enclosed in an incremental volume of 2 × 10^-⁹ m³ located at the origin is _________nC, if electric flux density of its field is found as

D = e^-^x sin $y \hat{i} - e^{- x} c o s y \hat{j} + 2 z \hat{k} C / m^{2} .$

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Vishal Baghel | Contributor-Level 10

a month ago

Using gauss law in differential form

$\vec{\nabla} . \vec{E} = \frac{ρ}{ε_{0}}$

$\vec{\nabla} . (ε_{0} \vec{E}) = ρ$

$\Rightarrow \vec{\nabla} . \vec{D} = ρ$

$\Rightarrow (\frac{\partial}{\partial x} \hat{i} + \frac{\partial}{\partial y} \hat{j} + \frac{\partial}{\partial z} \hat{k}) . \vec{D} = ρ$

$\begin{array}{l} \Rightarrow ρ = - e^{- x} s i n y + e^{- x} s i n y + 2 = 2 \\ \Rightarrow Q = 2 (V o l u m e) = 4 \times 1 0^{- 9} c = 4 n c \end{array}$

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The total charge enclosed in an incremental volume of 2 × 10^-⁹ m³ located at the origin is _________nC, if electric flux density of its field is found as

D = e^-^x sin $y \hat{i} - e^{- x} c o s y \hat{j} + 2 z \hat{k} C / m^{2} .$

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The total charge enclosed in an incremental volume of 2 × 10-9 m3 located at the origin is _________nC, if electric flux density of its field is found as D = e-x sin y i ^ − e − x c o s y j ^ + 2 z k ^ C / m 2 .

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The total charge enclosed in an incremental volume of 2 × 10^-⁹ m³ located at the origin is _________nC, if electric flux density of its field is found as

D = e^-^x sin $y \hat{i} - e^{- x} c o s y \hat{j} + 2 z \hat{k} C / m^{2} .$