Magnetic field of an infinite cyliner of fixed magnetization

[gabbagabbahey]

Just to be clear, I think you should calculate the field using Ampere's law in terms of B and J_b for part (a). And then calculate it again using Ampere's law in terms of H for part (b).

I think the point of the question is to illustrate that using Ampere's Law in terms of H is often quicker than using it in terms of B; since for the former you don't need to know the bound currents, while for the latter you do.

 

[insynC]

Yeah that makes sense. Unfortunately, our lecturer laboured the expression for A that I was using, so I'm not sure what exactly was wanted.

But I'll do what you said, thanks.

 

[Cyb]

I have been struggling with this problem. I can get the equivalent expressions for most everything, what I can't understand is the Ampere's loop of the B field using the current density J_b. The differential area vector would always be in the z direction if we wanted B to be constant over the line, but J_b points in the phi direction. Thus J_b o da' will be zero, and then B=0 even when r<R. Can someone please help me??

 

[gabbagabbahey]

I have been struggling with this problem. I can get the equivalent expressions for most everything, what I can't understand is the Ampere's loop of the B field using the current density J_b. The differential area vector would always be in the z direction if we wanted B to be constant over the line, but J_b points in the phi direction. Thus J_b o da' will be zero, and then B=0 even when r<R. Can someone please help me??

Hi cyb, welcome to PF!

What are you using as your Amperian loop and why?

 

[Cyb]

I think I figured it out. I was using circles, with centers at the axis of symmetry for the cylinder. On thinking about it more I came to a rectangle, whose long sides are parallel to the cylinder's axis, the top was outside of the cylinder and the bottom inside. Thus, B=0 outside, and since B has to be in the direction of the axis the only non-zero part of the loop is the length inside. Then using my current density and surface current for the intersected area I came up with the correct answer. Does that seem right?

 

[gabbagabbahey]

I think I figured it out. I was using circles, with centers at the axis of symmetry for the cylinder. On thinking about it more I came to a rectangle, whose long sides are parallel to the cylinder's axis, the top was outside of the cylinder and the bottom inside. Thus, B=0 outside, and since B has to be in the direction of the axis the only non-zero part of the loop is the length inside. Then using my current density and surface current for the intersected area I came up with the correct answer. Does that seem right?

Sounds good!