# Why magnets H field oposes its B

1. Sep 23, 2013

### si22

hi is there a basic way to picture how the H field inside a permanent magnet opposes its B field (i know the eq's are made to say it does just how to visulize this)

-ie H seems to be the magnets atomic dipoles which aline with B & not against it. also does the H oppose B inside an empty coil. thanks much

2. Sep 23, 2013

### clem

H is a mathematical field defined by H=B-4pi M (in gaussian units).

3. Sep 23, 2013

### si22

thanks for the reply i know the formula says this, & was just wondering how to best visulize the H vector

which suposidly is caused by the atomic dipoles -& yet oposes these dipoles? or is H just a math type shortcut

Last edited: Sep 23, 2013
4. Sep 23, 2013

### Jano L.

Since in the static case,

$$\mathbf H = \mathbf B/\mu_0 - \mathbf M$$

$$\nabla\times\mathbf H = 0,$$
it follows that the field H can be imagined as a potential field. Since

$$\nabla\cdot \mathbf H = -\nabla \times \mathbf M,$$
which is nonzero only at the faces on the ends of the bar magnet, the field H can be regarded as generated by a pair of magnetic poles located at those ends; the lines of the field originate in the N pole and get absorbed in the S pole, similarly to the electric field of an electric dipole. Inside the magnet, the field H points from N to S.

However, for the B field,

$$\nabla\times\mathbf B \neq 0,$$
so it is not a potential field and cannot be imagined as due to poles. Outside the magnet, the B and H field are always proportional. However, since

$$\nabla *\cdot \mathbf B = 0,$$

the B field has no sources and thus tranverse the faces of the magnet withotu change. Hence due to continuity, the B field inside the magnet points from S to N.

So inside the magnet, the two fields point in the opposite directions.

5. Sep 26, 2013

### si22

thanks for all the great answers & just to clarify a few things since i know just a bit about the curl & div etc

for ex. 1) if theres a magnet with just one atomic dipole & you compare the H & B side by side
obviosly the dipoles B field looks like a standard magnet
in part because the div B = 0, & ie B does infact curl

2) but just because the formula says H = B/u0 - M
why does that lead to curl H = 0
& why does that lead to H being a potental field
& even if it is why automaticly does that say H divs
(& not for ex. curls like the real vector potental A)

3) & why this div H said to oppose curl M
-& how does M even curl & not div when its in same units as H ie a/m
& how is H only nonzero at ends of magnet

4) & how can H even posibly act like a point source if ie its like the applied field in a BH curve that alines B in the first place.
& does any of this make any difference if its a coil or just
an atomic dipole

5) also why if the curl of B = nonzero means its not a potential field
yet when the curl of vector potental A = nonzero it is a
potential field?
& just for review how is a potential field differnt than a regular field ie is it mainly because its related to potential energy? & if so dont alot of fields have potential energy ex B etc again thanks much for all the help

6. Sep 27, 2013

### clem

H is NOT caused by the atomic dipoles, and is just a math type shortcut.

7. Sep 29, 2013

### Hassan2

You are referring to the demagnetizing field of a permanent magnet. The correct statement is: the magnet H field opposes its magnetization (that's why it is called the demagnetizing field). To understand why it opposes the magnetization, assume a permanent magnet as an ensemble of numerous tiny bar magnets parallel with one another. At each point inside the permanent magnet, the magnetic field is the superposition of the fields of all the tiny bar magnets. As you can imagine, the fields due to the magnet bars surrounding the point from sides, are opposite to the their magnetization ( because the field lines return outside the bars to close). The field due to the bars on the top and bellow the point are in the same direction of their magnetization but the effect of the fields from the sides is stronger. This fact can be considered for all the tiny bars and we find out that the total field is in the opposite direction of the magnetization of the magnet.