- #1

fluidistic

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## Homework Statement

Describe the following vector field: [tex]\bold v (\bold x)=\frac{\bold a \times \bold x}{(\bold a \times \bold x)(\bold a \times \bold x)}[/tex] with [tex]\bold a = \text{constant}[/tex].

Calculate its divergence and curl. In what region is there a potential for [tex]\bold v[/tex]? Calculate it.

Hint: Use cylindrical coordinates in which [tex]\bold a[/tex] is an axis.

## Homework Equations

None given.

## The Attempt at a Solution

I don't really know how to use the hint. I've calculated [tex]\bold a \times \bold x[/tex] to be worth [tex](a_2 x_3-x_2a_3) \hat i -(a_1x_3-a_3x_1) \hat j + (a_1x_2-a_2x_1)\hat k[/tex].

I wrote [tex]a_1=\rho \cos \varphi[/tex], [tex]a_2=\rho \sin \varphi[/tex] and [tex]a_3=a_3[/tex]. I'm stuck here, I have no idea about how to continue. I think I should write [tex]\bold x[/tex] in cylindrical coordinates but I don't know how that would help and there's no relation with [tex]\bold a[/tex].