The faces adhe, bcgf, cdhg and abfe will contribute zero flux because the area vector is normal to the electric field for these faces.
Flux through face efgh,ϕ = ∫ E . dA
= a(j) . [tex]l^{2}[/tex] (-j) = -a[tex]l^{2}[/tex]
as the field given at the face efgy is E =aj and the area vector is denoted as [tex]l^{2} (-j)[/tex]
Thus, flux through the face abcd,
ϕ2 = (a+bl)j .[tex]l^{2} (j) = al^2 + bl^3[/tex] for y = l
Thus net flux through the cube = ϕ1 + ϕ2 = b[tex]l^{3}[/tex]
From Gauss law, we know that ϕ = Qenclosed/[tex]\epsilon_{o}[/tex]
Qenclosed = [tex]\epsilon_{o}[/tex] ϕE = [tex]\epsilon_{o}[/tex]b[tex]l^{3}[/tex]
Thus, after substituting the values, we have l = 1m and b=3m
Qenclosed = 3 [tex]\epsilon_{o}[/tex]
The required figure for reference to the faces is attached below.
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