3.32 Let D = 2

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**Problem 3.32**

Let \(\mathbf{D} = 2 \rho z^2 \mathbf{a}_\rho + \rho \cos^2 \phi \mathbf{a}_z\). Evaluate

(a) \(\oint_S \mathbf{D} \cdot d\mathbf{S}\)

(b) \(\int_V \nabla \cdot \mathbf{D} \, dv\)

over the region defined by \(0 \leq \rho \leq 5\), \(-1 \leq z \leq 1\), \(0 < \phi < 2\pi\).
Transcribed Image Text:**Problem 3.32** Let \(\mathbf{D} = 2 \rho z^2 \mathbf{a}_\rho + \rho \cos^2 \phi \mathbf{a}_z\). Evaluate (a) \(\oint_S \mathbf{D} \cdot d\mathbf{S}\) (b) \(\int_V \nabla \cdot \mathbf{D} \, dv\) over the region defined by \(0 \leq \rho \leq 5\), \(-1 \leq z \leq 1\), \(0 < \phi < 2\pi\).
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