The volume charge density as a function of distance ‘x’ from one face inside a cube of side length ‘a’ varies as shown in the figure. Then the total flux in SI units through the cube is $\frac{n a^{2} ρ_{o}}{4 ε_{o}} .$ Find $n$ .

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answer is 3.

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Detailed Solution

From Gauss law, $Electric flux = \frac{Charge enclosed}{ε_{0}}$

$φ = \frac{\int ρ a^{2} d x}{ε_{0}} = \frac{a^{2} \int ρ d x}{ε_{0}} = \frac{a^{2} (a r e a u n d e r ρ - x g r a p h)}{ε_{0}} = \frac{3 a^{2} ρ_{0}}{4 ε_{0}} .$

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