Creating any shape of a magnetic field?

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Creating any specific shape of a magnetic field is constrained by Maxwell's equations, which dictate the behavior of magnetic fields in space. While magnetic fields extend infinitely, achieving a desired shape in a finite area is challenging and often impractical. Certain applications, like electron beam control in Cathode Ray Tube displays, have required innovative designs to manipulate magnetic fields effectively. However, the general question of shaping magnetic fields lacks a straightforward answer without specific parameters. Understanding these concepts typically requires a foundation in calculus for deeper insight.
Sebastian B
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I was wondering if it was possible to create any shape of magnetic field. If yes, what would it take to do so?
 
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What about if I wanted a certain magnetic field in a constrained/finite area?
 
Sebastian B said:
I was wondering if it was possible to create any shape of magnetic field. If yes, what would it take to do so?
No. The magnetic field is constrained by Maxwell's equations. For instance, it is impossible to create a maximum of the magnetic field in free space.
 
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Young physicist said:
Is it possible to understand that without calculus?(Sorry for trying to understand everything before knowing calculus)
Unfortunately, I don't think so.
 
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Sebastian B said:
I was wondering if it was possible to create any shape of magnetic field. If yes, what would it take to do so?
This question is far too general for a sensible answer. You haven't specified what you want but there are many applications foe magnetic fields that require some weird field patterns. I'm thinking, in particular, about the requirement to form well controlled beams of electrons in old fashioned Cathode Ray Colour display tubes. The original 'shadow mask' type tubes needed to use very long beam paths in order to make the RG and B beams properly converge and to get pure colours. Designers got more and more inventive with the shaping of the scanning magnetic fields and managed to achieve the same quality with ever shallower tubes with 'flatter' screens.
 
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