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The diagram shows a charged slab that has infinite length in the $x$ and $z$ directions. The slab's height in the $y$ direction is $2D$. The slab carries a nonuniform charge that depends on $y$-coordinate according to the function $\rho = Cy^2$.

A Gaussian surface in the form of a rectangular prism is also shown in the diagram. This Gaussian surface has base area $A$ and height $d$ and is oriented so that the faces with area $A$ coincide with the planes $y = 0$ and $y = d$.

Which of the following expresses the charge enclosed in the Gaussian rectangular prism?

A

$3\,C\,A\,{d}^{2}$

B

$\dfrac{1}{3}\,C\,A\,{d}^{3}$

C

$\dfrac{1}{2}\,C\,A\,{d}^{2}$

D

$\,C\,A\,{d}^{2}$

E

$2\,C\,A\,{d}^{2}$

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