# Why magnets H field oposes its B

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

Meir Achuz
Homework Helper
Gold Member
H is a mathematical field defined by H=B-4pi M (in gaussian units).

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:
Jano L.
Gold Member
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.

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

Meir Achuz