- #1
YogiBear
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Homework Statement
The gradient, divergence and curl in spherical polar coordinates r, ∅, Ψ are
nablaΨ = ∂Φ/∂r * er + ∂Φ/∂∅ * e∅ 1/r + ∂Φ/∂Ψ * eΨ * 1/(r*sin(∅))
nabla * a = 1/r * ∂/∂r(r2*ar) + 1/(r*sin(∅)*∂/∂∅[sin(∅)a∅] + 1/r*sin(∅) * ∂aΨ/∂Ψ
nabla x a =
|er r*e∅ r*sin(∅)*eΨ |
|∂/∂r ∂/∂∅ ∂/dΨ |
| 1/r2*sin(∅) |ar r*a∅ r*sin(∅)*aΨ |
Where a = ar * er + a∅*e∅ + aΨ*eΨ
Suppose that the vector field w has the form w = wΨ(r, ∅) eΨ Show that w is
solenoidal and find wΨ(r, ∅), when w is also irrotational. Find a potential for w in this case.
Homework Equations
The Attempt at a Solution
I started by finding vector potential. however it seems too simple. (Or most likely id id it wrong). In addition i am not sure, if it is even the right way to about it. I can't put in working out of the vector potential i have, as i have trouble with coding it on the forum(My handwriting is not legible). So you can assume i have got it wrong. Any help will be greatly appreciated.