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The electric field components in the figure $E_{x} = α x^{1 / 2}, E_{y} = E_{z} = 0$ If $α = 800 N m^{- 2}$ and a =0.1 m is the side of cube, then the charge within the cube is in ( pC)(Rounded off to the nearest integer)

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answer is 9.

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Detailed Solution

Flux at the surface $ϕ_{2 a} = a^{2} \times (α {(2 a)}^{\frac{1}{2}})$

$ϕ_{2 a} = α \sqrt{2} . a^{2.5}$

$ϕ_{a} = {αa}^{2.5}$

Total flux = ${αa}^{2.5} (\sqrt{2} - 1)$
We know $ϕ = \frac{q}{ε_{0}} \Rightarrow q = {αa}^{2.5} (\sqrt{2} - 1)$
$\Rightarrow q = 800 \times {(0.1)}^{2.5} (\sqrt{2} - 1) \times 8.85 \times 10^{- 12} = 9 pC$

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