Question 671: Electrostatics & Capacitance

Question

The total charge enclosed in an incremental volume of 2 $$	imes$$ 10
$$-$$9
m
3
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/m
2

Accepted Answer

$$\overline D  = {\varepsilon _0}\overline E $$
$$Div.\,\overline E  = {ho  \over {{\varepsilon _0}}}$$
$$ \Rightarrow div.\,\overline D  = ho $$
$$ \Rightarrow {\partial  \over {\partial x}}\left( {{e^{ - x}}\sin y} ight) + {\partial  \over {\partial y}}\left( { - {e^{ - x}}\cos y} ight) + {\partial  \over {\partial z}}(2z) = ho $$
$$\Rightarrow$$ $$ho$$ = 2 (a constant)
V = 2 $$	imes$$ 10
$$-$$9
m
3
q = 2 $$	imes$$ 2 $$	imes$$ 10
$$-$$9
= 4 nC

Electrostatics & Capacitance

The total charge enclosed in an incremental volume of 2 $\times 10 -9 m 3 located at the origin is ___________ nC, if electric flux density of its field is found as D = e -x sin y \widehat i - e -x cos y \widehat j + 2z \widehat k$ C/m 2

Integer / Numeric Answer Type