JEE MAIN - Physics (2021 - 22th July Evening Shift - No. 23)
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
D = e$$-$$x sin y $$\widehat i$$ $$-$$ e$$-$$x cos y $$\widehat j$$ + 2z $$\widehat k$$ C/m2
Answer
4
Explanation
$$\overline D = {\varepsilon _0}\overline E $$
$$Div.\,\overline E = {\rho \over {{\varepsilon _0}}}$$
$$ \Rightarrow div.\,\overline D = \rho $$
$$ \Rightarrow {\partial \over {\partial x}}\left( {{e^{ - x}}\sin y} \right) + {\partial \over {\partial y}}\left( { - {e^{ - x}}\cos y} \right) + {\partial \over {\partial z}}(2z) = \rho $$
$$\Rightarrow$$ $$\rho$$ = 2 (a constant)
V = 2 $$\times$$ 10$$-$$9 m3
q = 2 $$\times$$ 2 $$\times$$ 10$$-$$9 = 4 nC
$$Div.\,\overline E = {\rho \over {{\varepsilon _0}}}$$
$$ \Rightarrow div.\,\overline D = \rho $$
$$ \Rightarrow {\partial \over {\partial x}}\left( {{e^{ - x}}\sin y} \right) + {\partial \over {\partial y}}\left( { - {e^{ - x}}\cos y} \right) + {\partial \over {\partial z}}(2z) = \rho $$
$$\Rightarrow$$ $$\rho$$ = 2 (a constant)
V = 2 $$\times$$ 10$$-$$9 m3
q = 2 $$\times$$ 2 $$\times$$ 10$$-$$9 = 4 nC
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