In a solenoid, the field lines within are relatively constant and parallel, and so, the magnetic field is strongest as compared to the poles, at which the field lines diverge. In a permanent magnet, however, the magnetic field is strongest at the poles, despite being the point of divergence of the field lines. Why?
[Physics] Why is the magnetic field strongest at the poles in a permanent magnet
magnetic fields
Related Solutions
This question was cross-posted on Electronics Stack Exchange. Here is my answer from over there:
Exactly what charged particles are flowing outside (and inside) a permanent magnet that create the magnetic "lines"?
The magnetic field of a permanent magnet is not caused by flowing particles.
The electrons within a ferromagnetic material, even if they aren't flowing, have quantum mechanical spin. If the spin vectors of many of the electrons within the material are aligned, they produce a net magnetic dipole moment, producing the macroscopic magnetic field lines associated with a permanent magnet.
(This is just another way of saying, even when electrons aren't moving, they produce a magnetic field. We don't really know "why" that is, but we have a mathematical model of how much field they produce and how it interacts with other objects, and we call that model the "spin" of the electron).
You can read more about this in the Wikipedia article on Ferromagnetism.
Do those particles come from something inside the magnet or does the magnet do something outside of it to affect unknown particles to make the lines?
It comes from the electrons in the magnetic material.
If there is a current (i.e. a continuous flow of charged particles), then why don't we harness that current like a water wheel
Since the magnetic field doesn't derive from the flow of particles, we can't harvest it as if it were a flow of particles.
We measure B in terms of Newtons/meter/Ampere ... Consequently, those "magnetic lines" are currents (or flows) of charges
The B-field has amperes in its units because it produces a force on a moving charge according to the Lorentz law:
$$\vec{F}=q\vec{v}\times{}\vec{B}$$
Since it is multiplied by a charge and a velocity to produce a force, it must have units $\dfrac{[\mathrm{N}][\mathrm{s}]}{[\mathrm{C}][\mathrm{m}]}$ in order for the equation to balance.
Just as a force itself has $[\mathrm{kg}]$ in its units because it has an effect on something with mass, although a force does not have mass itself; a B-field must have charge in its units because it effects charges, not because it is composed of charge or contains charge.
The lines are indeed visualisations to represent a vector field.
At each point in space there is a magnetic field strength and a direction for that field.
The left hand diagram is such a representation for the magnetic field around a current carrying conductor with the current coming out of the screen.
If it was correctly drawn then the length of each of the arrows should be inversely proportional to the distance from the centre.
So this diagram gives you information about magnitude and direction.
The representation that you are perhaps more familiar with is thet in the right when the tangent to a field at a point gives the direction of the magnetic field line.
To illustrate the fact that the field is stronger near the conductor the concentric circles are drawn closer to one another.
So perhaps the second diagram does not have as much information on it as the first but it is significantly easier to draw.
However there diagrams are incomplete in that the magnetic fields are actually three dimensional and then the drawing of such diagrams becomes even more difficult.
Historically the magnetic flux density was the number of field lines per unit area and that is were the term flux (= flow) comes from with magnetic flux being the total number of lines.
You will still find lots of textbooks which are in esu, emu, cgs and Gaussian units from a time when there were also magnetic poles which followed an inverse square law just like Coulomb's law for electric charges.
So going back to your queries and the statement you made that they the magnetic field lines are visualisations and so you have some degree of artic licence with them provided you follow the simple properties:
Start and finish on themselves although it is often much clearer if you have them starting on a North pole and finishing on a South pole.
The arrow on a magnetic field line goes away from a North pole and goes towards a South pole or follows the right hand grip rule for currents.
Magnetic field lines are in a state of tension. That is why a North pole attracts a South pole!
- Magnetic field lines never cross and repel each other. That is why two North poles repel one another!
- The closer the lines are to one another the stronger is the magnetic field (magnetic flux density).
Best Answer
When we talk about a magnet's field being strongest at the poles, we're comparing the strengths of field at points outside the magnet. If we similarly restrict ourselves to points outside a solenoid, then the field is strongest at its ends (where the field lines have hardly started to diverge). We must compare like with like!