1. The problem statement, all variables and given/known data 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. 2. Relevant equations 3. 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.