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The box-like Gaussian surface shown in Fig. 23-56 encloses a net charge of \( +32 \varepsilon_{0} \mathrm{C} \) and lies in an electric field given by \( \vec{E}=[(10.0+2.00 x) \hat{\mathrm{i}}-3.00 \hat{\mathrm{j}}+b z \hat{\mathrm{k}}] \mathrm{N} / \mathrm{C} \), with \( x \) and \( z \) in meters and \( b \) a constant. The bottom face is in the \( x z \) plane; the top face is in the horizontal plane passing through \( y_{2}=1.00 \mathrm{~m} \). For \( x_{1}=1.00 \mathrm{~m}, x_{2}=4.00 \mathrm{~m} \), \( z_{1}=1.00 \mathrm{~m} \), and \( z_{2}=3.00 \mathrm{~m} \), what is \( b \) ?
Figure 23-56 Problem 25.
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