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.

 

[asteriatic]

Hello,

Thank you for your question.

It is difficult to provide a specific response without further context or information about the figure and equations being referenced. However, in general, the use of (z' - z) and dz' in an integration problem involving a uniformly magnetized cylinder could indicate a change of variable or coordinate system. The ' symbol typically represents a primed variable, which is often used to differentiate it from the original variable. This could be used to simplify the integration process or to switch from one coordinate system to another (e.g. from Cartesian to cylindrical coordinates).

Without seeing your specific attempt at the solution, it is difficult to say if it is wrong or not. However, it is possible that your approach using a differential dz and integrating from 0 to L may also be valid. It ultimately depends on the specific problem and the method used to solve it. If you are unsure about your solution, it may be helpful to consult with your instructor or a classmate for clarification.

I hope this helps. Good luck with your studies!

Best,