Uniformly Magnetized Cylinder (B/H Field)

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,

$$(z' -z) \quad \text{ and } \quad dz'$$

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

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

Uniformly Magnetized Cylinder (B/H Field)

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