What Defines a Solenoidal Vector Field?

tweedle2
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Homework Statement
So I know how to work out if a vector field is incompressible normally, the divergence is 0. However I don't know how to do it for cylindrical or spherical coordinates, can anyone help me
Relevant Equations
Div f = 0
ac.PNG
 
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(a) The polarisation pattern is elliptical with maximum (1,1) and minimum (-1,-1), and anticlockwise in direction. (b) I know the solution is a quarter-wave plate oriented π/4, and half-wave plate at π/16, but don't understand how to reach there. I've obtained the polarisation vector (cos π/8, isin π/8) so far. I can't find much online guidance or textbook material working through this topic, so I'd appreciate any help I can get. Also, if anyone could let me know where I can get more...

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