Magnetic field inside a material

In summary: M field equal to µoBnow consider any solenoid in any region Rits current Ii will cause a magnetic moment M inside it, and the field lines of that solenoid will intersect the B field lines at point Mthat field M is the same as µoB, because µoB=µoniM
  • #1
jd12345
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IF a material say a ferromagnet is placed in a magnetic field Bo then there will be an additional field due to ferromagnet which is equal to uoM (M is magnetisation)

My doubt is how is the additional field equal to uoM. By considering the units of both this expression is indeed equal to the magnetic field but still I'm not convinced

M is magnetisation which is total dipole moment in the material divided by volume. And if we multiply it by uo we get the magnetic field produced by it?? I'm very unconvinced by this. I just can't believe stuff with no proofs
So please help me - give me an intuitive proof or something so that my mind is convinced
 
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  • #2
You talk abou the additional field, additional to what?

Well, in a ferro-magnetic material, B=u0(H+M) , where H=Hd+Ha. Hd is called the demagnetizing field and Ha is the applied field. The difference is then u0(Hd+M), which is less than B=u0M because Hd has a negative effect on B. Hd depends on the geometry of the material and on M. For a uniformly magnetized sphere, Hd=-1/3*M

In order to understand Hd, imagine numerous magnet bars ( in fact, the magnetic dipoles) parallel and packed, with the same polarity. The field lines of each bar closes through the fields of other magnets and attenuates them. We can reduce this Hd to zero by making a closed magnetic circuit with no gap.
 
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  • #3
hi jd12345! :smile:
jd12345 said:
… how is the additional field equal to uoM. By considering the units of both this expression is indeed equal to the magnetic field but still I'm not convinced

M is magnetisation which is total dipole moment in the material divided by volume. And if we multiply it by uo we get the magnetic field produced by it??

see http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/solenoid.html :smile: for a visual demonstration of the connection between magnetic field and magnetic (dipole) moment …

the magnetic field in empty space inside an ordinary electric solenoid (straight and long, or circular) with current I, and n turns per metre, is found experimentally to be B = µonI

but the magnetic moment density is, by definition, Mo = nI

so B = µoMo

(and H = Mo)​

this shows the relation between magnetic fields measured in tesla (T) and measured in ampere-metre (A-m) :wink:

(and if you put a magnetic core inside the solenoid, it will have induced magnetic moment density M, and the field will now be B = µo(Mo + M))
 
  • #4
tiny-tim said:
hi jd12345! :smile:(and if you put a magnetic core inside the solenoid, it will have induced magnetic moment density M, and the field will now be B = µo(Mo + M))

Sorry , I believe your last formula is incorrect except for an infinitely long core.

If you puts a cylinder core with length L inside an infinitely long solenoid, the B-field in the core is less than if you put a a cylinder with with length 2L. Your equation is not compatible with this fact.
 
  • #5
Hassan2 said:
Sorry , I believe your last formula is incorrect except for an infinitely long core.

yes, i said straight and long :smile:
 
  • #6
further thoughts :rolleyes:
jd12345 said:
M is magnetisation which is total dipole moment in the material divided by volume. And if we multiply it by uo we get the magnetic field produced by it?? I'm very unconvinced by this. I just can't believe stuff with no proofs
So please help me - give me an intuitive proof or something so that my mind is convinced

µo is a constant which should be "1" (see bottom)

the magnetic field is measured by its effect (via the Lorentz force), the magnetisation field is measured by its cause (induction by an actual or a theoretical system of currents in loops) …

if µo was "1", that link between cause and effect wouldn't be surprising

let's see a "visual" proof of that link:

any magnetic field can be replaced by an identical solenoidal field, as follows:

a solenoidal field is a region R of space with a "honeycomb" of thin hexagonal solenoids (they needn't be hexagonal: but that makes them fit nicely :wink:), each with a (different) current Ii, and a (different) pitch, ni (pitch is turns per length)

the solenoids aren't straight, they can be curved into any shape

that causes ("induces") the whole region R to be filled with a magnetic field, of "Lorentzian" strength µoniIi inside each solenoid

this is of course the same as µoMi, where Mi is the magnetic moment density of each solenoid, measured in amp-turns per metre

(magnetic moment per turn = IiA, where A is the cross-section area of that turn; so magnetic moment per volume = IiA times turns per volume = Ii times turns per length = Iini = Mi)​

now consider any B field in any region R

we can fill R with an imaginary honeycomb of solenoids whose sides follow the B field lines (ie lines of constant |B|, and whose tangent at each point is parallel to the B field at that point), and whose current or pitch (or both) are adjusted so that the solenoidal field equals the B field along the centre line of each solenoid …

and by making the number of solenoids large enough (ie, the diameters small enough), we can make the solenoidal field match the whole B field to any required degree of accuracy

in other words: in the limit, any actual B field can be replaced by a purely solenoidal field​

B fields are naturally measured by their effect, in units of force per charge per speed (N.s/C.m = N/A.m = tesla)

(we could call these either "Lorentzian units" (named after the Lorentz force q(E + v x B)), or "Laplacian units" (named after the Laplace force qv x B))

solenoidal fields are naturally measured by their cause, in units of magnetic moment density, measured in amp-turns per metre, or A-turn/m (or, in SI units, simply but confusingly :redface: A/m)

the conversion ratio between these cause and effect measurements is a universal constant, µo, which should be "1", in units of N/A2 (Newtons per amp per amp-turn) :smile:

why isn't this unit "1" ? :confused:

well, it would be :smile:, buuuut :rolleyes:

i] in SI units, a factor of 4π keeps cropping up! … so we multiply by 4π :wink:

ii] that would make the amp that current which in a pair of wires a metre apart would produce a force between them of 2 N/m …

which would make most electrical appliances run on micro-amps!

so, for practical convenience only, we make µo 107 smaller, and the amp 107 larger! :biggrin:

(so the amp is that current which in a pair of wires a metre apart would produce a force between them of 2 10-7 N/m, and µo is 4π 10-7 N/A2 (= 4π 10-7 H/m))

(for historical detaills, see http://en.wikipedia.org/wiki/Magnetic_constant)
 
  • #7
fair enough - thank you
 
  • #8
Thanks tiny-tim. Now I understand why a divergence-free field is called a solenoidal field.
 

FAQ: Magnetic field inside a material

What is a magnetic field?

A magnetic field is a region in space where a magnetic force can be detected. It is created by moving electric charges, such as the electrons in atoms and molecules.

How is a magnetic field inside a material created?

A material becomes magnetized when its electrons align in the same direction, creating a net magnetic field. This can be achieved through a variety of methods, such as exposing the material to a strong external magnetic field or heating it to a specific temperature.

What factors affect the strength of the magnetic field inside a material?

The strength of the magnetic field inside a material depends on the material's magnetic properties, such as its permeability and susceptibility. It also depends on the external magnetic field strength and the temperature of the material.

Why do some materials have stronger magnetic fields than others?

Some materials, such as iron, nickel, and cobalt, have strong magnetic fields because their electrons can easily align in the same direction and create a strong net magnetic field. Other materials, such as copper and aluminum, have weaker magnetic fields because their electrons cannot easily align.

How does the magnetic field inside a material affect its properties?

The magnetic field inside a material can affect its properties in various ways. For example, it can influence the material's mechanical strength, electrical conductivity, and chemical reactivity. It can also be used to manipulate and control the material's behavior, such as in magnetic storage devices and medical imaging techniques.

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