# Magnetostatics homework help

1. Nov 3, 2006

### pivoxa15

In my textbooks it shows curl of H = 0 is a situtaion of magnetostatics but in here http://en.wikipedia.org/wiki/Magnetostatics it shows otherwise assuming J can be anything. Which is correct?

Magnetostatics is defined to be when the magnetic field is constant so H should be a vector field with scalar components suggesting that curl of H=0.

2. Nov 3, 2006

### quasar987

curl of H will be 0 outside regions with currents.

3. Nov 3, 2006

### pivoxa15

I also should have mentioned that magnetic fields can only arise when a current is present. So a constant current must be present. But it means H will be a non constant field so can't be magnetostatics?

Outside regions with current, magnetic fields don't even exist - which can't be magnetostatics can it? i.e. no charges is not electrostatics.

We seem to have a problem either way. What am I missing?

4. Nov 3, 2006

### quasar987

I wonder how you make that conclusion. It is readily seen from say Biot savard law, or Ampere law over a circle centered on the axis of a wire in which a steady current flows that the megnetic field is constant in time.

wahoo! Then how can a magnet work?! No, a steady current creates a steady magnetic field in all space.

5. Nov 3, 2006

### quasar987

The relation between the magnetic field and its div and curl is the following:

Open the doc file called "Question.doc" and replace F by H in that equation. The integrals are over the whole universe. The first integral is always 0 because the divergence of H is always 0. But you see that as soon as there is a curent somewhere in space, the the integral is non- vanishing.

The main lesson here is that $\nabla\cdot \vec{H}=0$ and $\nabla\times \vec{H}=0$ at some points $\vec{r}$ does not imply $\vec{H}(\vec{r})=0$. The value of H at some point depends on the value of J everywhere in space.

Last edited: Nov 3, 2006
6. Nov 3, 2006

### pivoxa15

I am thinking about the curl of H = 0 => constant vector field H => magnetostatics.

But on the website curl of H = nonzero constant current density => H is a nonconstant vector field => B is non constant vector field hence not megnetostatics.

The problem is the current density should not be 0 for anything to do with magnetics but that leads to nonconstant B field so no magnetostatics.

In classical physics, we are taught to think about magnets as having mini current loops inside hence with many magnetic dipoles meaning magnetised material.

Last edited: Nov 3, 2006
7. Nov 3, 2006

### quasar987

I think I've hit it now:

The curl operator has nothing to do with how B behaves in time! It says something about how H changes in space. Magnetostatic is by definition a case where B is constant in time, not where the magnitude of B is the same at all points in space.

Well exactly. A magnet's magnetic field is cause by its surface current. But the point is that it is a current that causes the field, but there is a non zero B field all around the magnet, not only where the current itself it.

Last edited: Nov 3, 2006
8. Nov 3, 2006

### pivoxa15

Okay that makes more sense now. But there is still the question why my textbook shows magnetostatics only when curl of H = 0. The book later addressed with the fact that there are no free current in magnetostatics, which means the B fields in magnetostatics are never generated by electrical coils but rather by the magnets themselves (bound currents). But you could set up a constant B field with electrical coils without a magnet in sight couldn't you?

Last edited: Nov 3, 2006
9. Nov 3, 2006

### Meir Achuz

Your problem is that this statement is wrong.
Magnetostatics means that all partial time derivatives are zero, so steady currents are allowed. The key equations are Curl H=4 pi j/c and
div j=0.

10. Nov 3, 2006