Quick [Y/N] Q: Possible equations for B-fields?

[starrymirth]

Hi there, I'm going over a past electromagnetics exam paper, and had a quick conceptual question:

Homework Statement

A certain field is given in spherical coordinates by

\vec{B} = \frac{4 sin\varphi}{r^{2}} \hat{r} + [sin\theta + \frac{cos^{2}\theta}{sin\theta}] \hat{\theta} - 4r sin\theta \hat{\varphi} --(1)

Show that this is a possible magnetic induction.

Homework Equations

\nabla \cdot \vec{B} = 0 --(2)

The Attempt at a Solution

My question is, if equation (2) holds with the given B, is that sufficient? Are there any other conditions that must be met for (1) to be physically possible?

The thing that threw me here - is that it's out of 21 marks (~3marks per line/equation/fact, so 7 lines of working), and div B in spherical coordinates is a little tricky, but not that tricky. We're even given div for spherical coordinates on our formula sheet, so it made me think I might be missing something.

Thanks!
Laura

 

[grey_earl]

That should be all. Maybe they just want to be nice with you :)
Of course, you could also calculate curl B = j and check that j is "reasonable". But for me, that's not necessary.