Uniformly Magnetized Cylinder (B/H Field)

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Homework Statement



See figure attached.

Homework Equations





The Attempt at a Solution



Can someone explain to me why he uses,

[tex](z' -z) \quad \text{ and } \quad dz'[/tex]

What is the meaning of the ' ?

When I did this question, I preformed the integration with the limits from 0 to L with the z in tact using a differential dz.

Is that wrong?
 

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Answers and Replies

  • #2
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Still looking for some help!
 
  • #3
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He's using [itex]z[/itex] to be the coordinate of the point where we want to calculate the magnetic field, and using [itex]z'[/itex] to be the coordinate of the current loop. The distance from the current loop to the point is [itex]z - z'[/itex], but he probably skipped a step and used [itex]z' - z[/itex] instead because [itex](z-z')^2 = (z' - z)^2[/itex]. To consider the effects of all the loops from coordinate [itex]0[/itex] to [itex]L[/itex], you have to integrate w.r.t. [itex]z'[/itex] from [itex]0[/itex] to [itex]L[/itex].

If you've integrated w.r.t. [itex]z[/itex] from [itex]0[/itex] to [itex]L[/itex], then you've found the magnetic field at coordinate [itex]0[/itex], but you haven't found the magnetic field at a general coordinate [itex]z[/itex].
 
  • #4
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He's using [itex]z[/itex] to be the coordinate of the point where we want to calculate the magnetic field, and using [itex]z'[/itex] to be the coordinate of the current loop. The distance from the current loop to the point is [itex]z - z'[/itex], but he probably skipped a step and used [itex]z' - z[/itex] instead because [itex](z-z')^2 = (z' - z)^2[/itex]. To consider the effects of all the loops from coordinate [itex]0[/itex] to [itex]L[/itex], you have to integrate w.r.t. [itex]z'[/itex] from [itex]0[/itex] to [itex]L[/itex].

If you've integrated w.r.t. [itex]z[/itex] from [itex]0[/itex] to [itex]L[/itex], then you've found the magnetic field at coordinate [itex]0[/itex], but you haven't found the magnetic field at a general coordinate [itex]z[/itex].

Is there any other way you can reason this problem out without using the z'?

I'd like to see the other perspectives if there are any.
 

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