Uniformly Magnetized Cylinder (B/H Field)

• jegues
Still looking for some help!In summary, the student is trying to find the magnetic field at a general coordinate z by integrating w.r.t. z'. However, he may have skipped a step and used z' - z instead. To find the magnetic field at a specific coordinate z, he would have to integrate w.r.t. z from 0 to L.

Homework Statement

See figure attached.

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?

Attachments

• 2008FQ2.JPG
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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 $z$.

omoplata said:
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.