Uniformly Magnetized Cylinder (B/H Field)

jegues

1. The problem statement, all variables and given/known data

See figure attached.

2. Relevant equations



3. 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?

Attached Thumbnails

 

jegues

Still looking for some help!

omoplata

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].

jegues

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.