Uniformly Magnetized Cylinder (B/H Field)

[jegues]

Homework Statement

See figure attached.

Homework Equations

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?

 

[jegues]

Still looking for some help!

 

[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.

 

[jegues]

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.