Iam very confused that why not all field lines emanate out of a pole? Why few field lines emanate and in middle of a bar magnet as shown in the following figure:
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2 Answers
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The magnetic field of a bar magnet is made up from the individual magnetic dipoles of the outermost electrons in the iron atoms. The magnetic field of an individual electron is tiny, but since there are gazillions of electrons in a typical bar magnet their fields combine to generate a substantial overall field.
If you looked at the field from a single electron it would look a bit like:
so the field lines do splay out sideways as well as forwards and backwards. However in a collection of electrons the field from any given electron interacts with the electrons in front of it and behind it, and the result is to channel the field lines:
I fear my drawing skils don't do the subject justice, but hopefully the general idea is clear. When you have a bar magnet stuffed with electrons that are all lined up with each other then the field lines tend to run along the lines of the electrons so the only emerge at the ends of the bar magnet where the lines of electrons stop.
answered Mar 22, 2016 at 12:37
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$\begingroup$ The strength of the sideway field has to do with the saturation of the magnetic field on the poles, hasn't it? $\endgroup$ Commented Mar 22, 2016 at 19:03
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Why should they? :)
If the magnet is infinitely long, you will have no field lines escaping through the mantle, simply out of symmetry considerations.
But for a magnet of finite size the field will be less strong at the ends than in the center. This sounds logical, doesn't it. And it implies, that the density of field lines has to be less in the ends, which means that they have to have escaped in between.
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$\begingroup$ Asfaik field is stronger at poles, then ? $\endgroup$– JM97Commented Mar 22, 2016 at 11:29
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$\begingroup$ No, the field is stronger in the middle of the coil you have in the picture. In fast, the field in the middle is twice as strong as in the ends $\endgroup$– IljaCommented Mar 22, 2016 at 11:38
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$\begingroup$ But according to my textbook(pg.no-179, example 5.3d solution) field is stronger at poles. Could you provide any citations for your argument? Link of my textbook: ncert.nic.in/ncerts/l/leph105.pdf $\endgroup$– JM97Commented Mar 22, 2016 at 11:49
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$\begingroup$ now I read what you mean. This is a misunderstanding. Your drawing is a solenoid. There, the field is maximal in the middle (inside!). In a bar magnet you cannot get to the inside, this is the difference. Outside the solenoid/magnet the field is weak at the center. You see it in the picture: there are few field lines escaping there. Half of the field lines which are there in the center leave through the ends, the rest is spread over the long mantle and is therefore less dense = weak field $\endgroup$– IljaCommented Mar 22, 2016 at 13:04
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$\begingroup$ no, I can't provide a citation, but I can explain the factor 2 I mentioned: if you take two such solenoids at the ends together, you have only one long one, in which the former ends are in the new center. That's how you can see that the field is double in the center. $\endgroup$– IljaCommented Mar 22, 2016 at 13:10