Walker, Halliday & Resnick — Gauss' Law: Problem 34

34 The box-like Gaussian surface shown in Fig. 23-39 encloses a net charge of \(+32\epsilon_0\) C and lies in an electric field given by \(\vec{E} = [(10.0 + 2.00x)\hat{i} - 3.00\hat{j} + bz\hat{k}]\) N/C, with \(x\) and \(z\) in meters and \(b\) a constant. The bottom face is in the \(xz\) plane; the top face is in the horizontal plane passing through \(y_2 = 1.00\) m. For \(x_1 = 1.00\) m, \(x_2 = 4.00\) m, \(z_1 = 1.00\) m, and \(z_2 = 3.00\) m, what is \(b\)?