A uniform magnetic field (mathbf{B}) has constant strength (b) in the (z)-direction [i.e., (mathbf{B}=langle 0,0, bangle) ].
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A uniform magnetic field \(\mathbf{B}\) has constant strength \(b\) in the \(z\)-direction [i.e., \(\mathbf{B}=\langle 0,0, bangle\) ].
(a) Verify that \(\mathbf{A}=\frac{1}{2} \mathbf{B} \times \mathbf{r}\) is a vector potential for \(\mathbf{B}\), where \(\mathbf{r}=\langle x, y, 0angle\).
(b) Calculate the flux of \(\mathbf{B}\) through the rectangle with vertices \(A, B, C\), and \(D\) in Figure 19.
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