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My question is on the experimental setup of the Stern-Gerlach experiment, the model diagram in my textbook shows the magnetic field being created by a North pole and South pole magnet (I am assuming they are equal strength magnets, which may be incorrect).

Stern Gerlarch Apparatus

Upon examining this picture though I realized that the magnetic field gradient say $\frac{\partial B}{\partial z}$ would be positive in the upper half plane and negative in the bottom half. This is confusing me as I know the force on the magnetic dipole is proportional to the magnetic field gradient, thus I would expect that this would influence the deflection, but this isn't mentioned in the text. So I am wondering if anyone knows how this is reconciled, or if perhaps in the real experiment the magnetic field was actually generated such that the gradient is constant in one direction throughout the region.

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  • $\begingroup$ I'm a little unclear on your description and how it's confusing you, the field in the picture has a gradient only in the z direction as required, and this is what deflects the silver atoms used. Also you should state what text your talking about so there is some context. $\endgroup$
    – Triatticus
    Jan 10, 2022 at 7:09
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    $\begingroup$ What is a North pole magnet? $\endgroup$
    – DJohnM
    Jan 10, 2022 at 7:20
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    $\begingroup$ It is unclear why you think the magnetic field gradient is "positive in the upper half and negative in the bottom half". You can improve the question by clarifying why you think that. $\endgroup$
    – fishinear
    Jan 10, 2022 at 12:54

2 Answers 2

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The magnetic flux lines are shown to be diverging from N to S, so the B-gradient will have the same sign along the mid-plane. Independent of the invalidity of your assumption, I think the sign of the gradient does not play a role for the experiment outcome because there are both spins with equal probabilty in the incident beam.

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(a) The pieces of metal marked 'N' and 'S' are pole-pieces of a magnet, the main body of which is not shown. I've sometimes wondered, myself, just how stylised this standard textbook diagram is.

(b) I don't understand about $\frac{\partial B_z}{\partial z}$ changing sign. Surely it's always negative in the gap between the poles, taking the $z$ direction as downwards (or upwards!). I think that the 3 black lines coming from the pointy bottom of the North Pole and diverging are representative magnetic field lines.

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    $\begingroup$ the diagram is just simplified for the sake of clarity. If these were really two separate magnets, then they would both have a 'S' pole at the top and a 'N' pole at the bottom. However, as @Philip Wood says, in reality these will just be the pole-pieces of a single magnet the body of which is not shown. $\endgroup$
    – Martin CR
    Jan 10, 2022 at 12:01

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