3.56 Determine if each of the following vector fields is solenoidal, conservative, or both: \mathbf{A}=\hat{\mathbf{x}} x^{2}-\hat{\mathbf{y}} y 2 x y \mathbf{B}=\hat{\mathbf{x}} x^{2}-\hat{\mathbf{y}} y^{2}+\hat{\mathbf{z}} 2 z \mathbf{C}=\hat{\mathbf{r}}(\sin \phi) / r^{2}+\hat{\phi}(\cos \phi) / r^{2} \mathbf{D}=\hat{\mathbf{R}} / R \mathbf{E}=\hat{\mathbf{r}}\left(3-\frac{F}{1+P}\right)+\mathbf{z} z \mathbf{G}=\hat{\mathbf{x}}\left(x^{2}+z^{2}\right)-\hat{\mathbf{y}}\left(y^{2}+x^{2}\right)-\hat{\mathbf{z}}\left(y^{2}+z^{2}\right) \mathbf{H}=\hat{\mathbf{R}}\left(R e^{-R}\right)

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