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Hello scienceforums community. I'd like to introduce myself to start because I am somewhat of a new member. I am a physics undergrad but I'm very fresh into the realm of physics. I would like to ask some questions I've had about magnetism in order to give some better insight into what it is exactly.

1) Of course when talking about magnetism you have to talk about electricity. The equation B = {(mu)(I)}/ {2(pi)r} is an equation used to compute the magnetic field induced by a current carrying wire. I was curious to know what exactly mu (the permeability constant) represents in the equation and what makes it so important.

2) When calculating the strength of a magnetic field induced by a current we use an equation like the one I mentioned in the first question. What equation do we use in order to compute the magnetic field strength of a permanent magnetic or a magnet without a magnetic field induced by a current?

3) What is the difference between the electrostatic force and the electromagnetic force?

4) With magnetic flux and Lenz's law, what actually is taking place on an atomic level for a current to be produced by a moving magnetic field? Also why does the area change the magnetic flux?

Hopefully these questions aren't too basic, I'm really just interested in finding thorough and intuitive explanations behind some of the answers for a better understanding of these concepts.

Edited by VeritasVosLiberabit
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Well, I can help with the first two.

The value of µ0 i.e. 4π×10−7 H·m−1 comes from the definition of the ampere

"the constant current that will produce an attractive force of 2 × 10–7 newton per metre of length between two straight, parallel conductors of infinite length and negligible circular cross section placed one metre apart in a vacuum"

It is almost impossible to calculate the magnetic field of a permanent magnet. People make magnets then measure the field.

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As John Cuthber implies, the value µ0 is tied in with the definitions of the SI unit system. It's a proportionality constant. But you have permeability values for other materials, too, which tells you how strongly you concentrate fields in that material, because you can have atomic magnetic moments line up with an external field. It's also tied in, along the with permittivity, with the speed of light.

The difference between electrostatic force and the electromagnetic force is that the former assumes all charges are fixed. i.e. static. The latter is more general, and allows for currents, which give magnetic fields. Electric fields transform to give you magnetic fields when you have motion.

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1) Engineer's answer: µ is important because it's near 10-6 so you better don't forget it...

Half-joke only, this happens from time to time, and because many design attempts with electromagnetism yield completely impractical figures, intuition doesn't always tell if it results from a mistake or because the goal was impossible.

µ represents the ability of the medium (including vacuum) to let the induction B go through easily. That is, B=µ*H. µ is often written as µ0R, or vacuum times relative permeability. H is often costly (current, size of permanent magnet) while B is often the desired effect, for instance to produce a voltage; then a big µ is desired.

2) If you have a magnetic circuit, which is generally the case, or if you magnet has a permeability µR>1, which was the case with AlNiCo, then you're sitting in the ink (as they say in German) to hand-compute the induction. That's a job for FEM software.

Present-day ferrite or Nd-Fe-B magnets have µR~1.1 so you might take 1.1 and, without an external magnetic circuit, the situation looks better. You only have µ=1 everywhere, and a portion of the Universe is magnetised. Then the magnetisation J coupled (vectorially) with 1/R3 gives you H or B; you can sum the contributions of all volume elements over the magnet.

J itself can be modelled as many tiny current loops, and then you can compute H from this current (using a formula for a loop, not a straight wire). It does even make some sense for the magnetic polarisation resulting from orbital moments, where the evolution of the electron's wave function's phase over angle and time has some attributes of a rotation, especially angular momentum (electron's mass) and magnetic ommentum (electron's charge) - but not other attributes, for instance the electron's probability of presence doesn't move, and the orbital doesn't radiate.

3) Static charges versus "moving" ones... Except that the spin produces a magnetic field without a movement.

4) Current in a conductor is a collective behaviour of electrons, the atomic scale isn't adequate.

Electromagnetism is never basic, for no-one... One has to develop his intuition despite electromagnetism is not intuitive. Qualitative understanding can he horribly complicated, in antennas for instance.

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