# What is the direction of magnetic field lines?

Ok, so I was studying about magnetism. And the book mentioned:

Magnetic field lines are directed from south pole towards the north pole and thus a closed and continuous curve is formed.

Here is an image from the book:

Then the diagrams indicated that magnetic field lines are directed from north pole towards the south pole.

Here are the diagrams:

Now which one do I believe? Both the images are from Selina Publishers' Physics...

• Magnetic field lines are closed loops. Inside the magnet they run from South Pole to North; outside they run from North Pole to South. Mar 16, 2021 at 12:34

Now which one do I believe?

You believe both. They are both correct and they do not contradict each other at all.

The text says that the lines go from south to north inside the magnet. The images show the lines going from north to south outside the magnet. The fact that magnetic field lines form continuous closed loops means that south to north inside the magnet implies north to south outside and vice versa.

Outside the magnet the lines of both the $${\bf B}$$ and $${\bf H}$$ fields are directed from the north pole to the south pole. The quoted text in your first image refers to to inside the magnet where the lines of $${\bf B}$$ are directed from the south pole to the north pole so as to form closed loops. (Mathematically this is because $${\rm div\,}{\bf B}=0$$, but if you are just learning the subject this statement won't mean much to you). The inside lines of $${\bf H}$$ however run from the north pole to the south, so they are opposite to the lines of $${\bf B}$$. Unfortunately both $${\bf B}$$ and $${\bf H}$$ are called the "magnetic field" in casual talk.

The $${\bf H}$$ field is defined as $${\bf H}=\frac 1 {\mu_0} {\bf B}-{\bf M}$$ where $${\bf M}$$ is the magnetization or more precisely the magnetic dipole moment per unit volume of the magnetic material. It's a mesure of how strongly the magentic material is magnetized.

Both $${\bf B}$$ and $${\bf H}$$ are useful, because they satisfy simple equations.

The diagram because they are directed from north to south

• Some explanation please... Mar 16, 2021 at 12:12
• The Direction is taken as a convention and the magnetic field lines are also just imaginary though they are useful and if you keep a compass near near a magnet then the Direction in which needles north pole points is the direction of magnetic field lines. Mar 16, 2021 at 12:15
• Hmm... Fine. Thank you! Mar 16, 2021 at 12:17

The direction of the magnetic field lines is the direction of the B-field. By convention they go from North to South.

Sometimes it seems confusing. Let's put a wire under a compass, so that it (the wire) has direction N-S, and the conventional current flows to North. The resultant magnetic field from the wire acting on the needle, according to the right hand rule, is directed to east. And the needle is deflected to the east indeed.

But what happened was a sum of 2 vectors: $$\mathbf B_{earth} + \mathbf B_{wire}$$.

We must conclude that in the case of the earth, the field lines go from (approximated geographic) South to North. And that the magnetic pole close to the geographic north pole is in reality a magnetic south pole.

That way it is explained why the needle deflects to east. Its field lines aligns in a way to be parallel to the net external field and with opposing direction.