Question 1: Gauss' Law: Electric field from surface chargeFor this problem, assume constants are all in SI units that are not shown. An electric field given by \(\vec{E} = (3z^3 + 5) \hat{k}\). Calculate the flux through surface \(S\), with side length \(a = 2\), shown below if the surface is at the following heights:(a) \(z = 0\)(b) \(z = -2\)(c) \(z = 2\)*Diagram*: A surface \(S\) is shown on the \(xy\)-plane with side length \(a\), positioned at various heights \(z\) with respect to the \(z\)-axis.(d) The electric field in a region is given by \(\vec{E} = a/(b + cx) \hat{i}\), where \(a = 500 \, \text{N} \cdot \text{m/C}\), \(b = 4.0 \, \text{m}\), and \(c = 1.0\). What is the net charge enclosed by the shaded volume shown below?*Diagram*: A rectangular prism is illustrated with dimensions \(2.0 \, \text{m}\), \(1.0 \, \text{m}\), and \(1.5 \, \text{m}\) along the \(x\), \(y\), and \(z\) axes respectively. The electric field \(\vec{E}\) is depicted with an arrow parallel to the \(x\)-axis.

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