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In a region of space, the electric field $\vec{E} = E_{0} x \hat{i} + E_{0} y \hat{j}$ . Consider an imaginary cubical volume of edge ‘a’ with its edges parallel to the axes of coordinates. Now (X axis is normal to 1&3, Y axis is normal to 2&4)

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total electric flux through the faces 1 and 3 is $E_{0} a^{3}$

total electric charge inside the cubical volume is $2 ε_{0} E_{0} a^{3}$

total electric flux through the faces 2 and 4 is $2 E_{0} a^{3}$

total electric charge in the cubical volume is $ε_{0} E_{0} a^{3}$

answer is A, B.

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Detailed Solution

$ϕ = \vec{E} . \vec{A} ϕ_{i n} = - v e a n d ϕ_{o u t} = + v e Q_{n e t} = \frac{q_{i n}}{ε_{0}} ϕ_{1} = 0, ϕ_{2} = E_{0} a^{3}, ϕ_{3} = E_{0} a^{3}, ϕ_{4} = 0, ϕ_{5} = 0, ϕ_{6} = 0$

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