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I am not a genius in magnetic field and how a magnet will interact with the field, but I was confused as to what the classical theory predicted when a magnet would be placed in a nonuniform magnetic field?

Also, why did the Stern-Gerlach experiment use a nonuniform magnetic field.

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The classical prediction is that the atoms, which are magnetic dipoles, will spread out into a single continuous smear instead of two distinct ones. In a magnetic field a magnetic dipole will experience a force and a torque.

The torque on the dipole depends on the magnetic field: $$\mathbf{\tau} = \mathbf{\mu} \times \mathbf{B},$$ and causes the magnetic moment to precess around (this is spin around) the magnetic field lines.

The force on the dipole depends on how the magnetic field is changing in space: $$\mathbf{F} = (\mathbf{\mu} \cdot \nabla) \mathbf{B}.$$ That's why the magnetic field has to be non-uniform - in order to generate a force.

Classically, the magnetic moments of the atoms coming out of an oven will be completely random, pointing in every direction with equal probability. So dipoles that point along the field gradient will experience a maximal force, and the majority will be (nearly) orthogonal to the gradient and experience no net force. What we see instead is that the atoms only experience forces as though they are completely aligned with or against the magnetic field, in the case of spin $1/2$ atoms. For atoms with higher total spin, the beam will split into more distinct groups if the ambient pressure is low enough: $3$ for spin $1$, $4$ for spin $3/2$, etc. This paper looks at the Stern-Gerlach spectrum of $\mathrm{O}_2$, and shows quite a complicated structure with many peaks.

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  • $\begingroup$ so is the magnetic dipole of electrons referred to as spin up and spin down? $\endgroup$
    – user510
    Oct 6, 2016 at 0:00
  • $\begingroup$ The magnetic dipole moment is generally proportional to angular momentum, and spin is a contributor to angular momentum. In the classical Stern-Gerlach experiment the atom is chosen so that the spin of the electron is the dominant contributor to the angular momentum. Oddly, spin contributes more than orbital angular momentum, but that's another topic. $\endgroup$ Oct 6, 2016 at 0:07
  • $\begingroup$ so what do they mean when they say spin up? I thought it referred to the magnetic dipole direction. And is magnetic dipole the same as magnetic moment? $\endgroup$
    – user510
    Oct 6, 2016 at 0:37
  • $\begingroup$ Spin is "up" if the total spin is $1/2$ and the spin angular momentum is in the same direction as the axis of measurement. If all of the angular momentum is spin, and you're dealing with an electron, then the magnetic moment of a spin up particle will be down because$$ \mathbf{\mu} = g \frac{q}{2m} \mathbf{S},$$ where $q$ is a particle's charge (negative for electrons) and $g$ is the g-factor. $\endgroup$ Oct 6, 2016 at 0:43
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this is my theory a magnet has a north and south pole which starts from static only 2 , that comes from mainly burning matter the electrons are released in the fire and are free to go there own way , so lets say theres hot and cold static these have a natural attraction when the first 2 collide the impact makes a magnetic pull which in turn attracts other static from the side. this slowly builds up to form matter in defferant geometric shapes due to side attraction angle which can vary upto 180 degrees from initial colision , each side. i beleive this is the basic build up of a magnet and a magnet attracts static and also gives off static . it attracts static from the north south pole and gives off static at an angle of 51degrees 51 minuets from the center north and south this tappers away from side of magnet criss crossing over each other as it goes toward neutral or lowest magnetic gravity area, this is a differant region than than the magnetic feilds its like a ring of saturn around the edge way out away from the magnetic core ,where the magnetic flux turns to static again but with direction around this ring ,when it does one orbit of this ring the flux decides to go back in to the magnetic center or out away from the magnet back to frree static . so if you picture this in your mind ,when the flux goes back in to the magnet for the first time from the ring it will decide to go north or south ,this is what makes north diferant from south because the ring flux goes there 2 and will stay in this arangment when you picture this image of the true magnetic shape you can see is an electrical worm that attracts its self ,every time one electon flows through the centre it pulses the whole feilds out like a pump ,if you can picture all the planets this ring of free static is where they all spin around the sun like spocketing together , note the pirimids pulled the earth to its magnetic centre they are built 51 degrees 51 minuets the top gives off free static which is adjustible in the kings chamber due to resignating frequency of the pyrimid though helium that wofts up from the queens chamber when activated this allowed ,i am getting to a point , this allowed the position of the moon to change if activated in the right time series ,so they could move the planet closer or futher from the sun , the static rings are real look at the facts

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  • $\begingroup$ Welcome on Physics SE. Your post is very hard to read due to missing formatting and loong run on sentences and I have a very hard time following what you are trying to tell us. Could you try to rewrite your answer to make it a bit more accessible? $\endgroup$
    – Sanya
    Oct 6, 2016 at 6:47

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