In a standard Cartesian coordinate system a charge \(q\) is placed at \((0,\frac{\sqrt{3}a}{2},0)\). If the absolute value of the flux due to this charge through the region

\[\frac{a}{2}<x<\frac{3a}{2}, y=0,-\infty<z<0\]

can be expressed as \(\displaystyle\frac{q}{C\epsilon_{0}}\) find \(C\).

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