Finding Vector potential due to an infinite cylinder?

[BeerScience]

Hi there,
2nd year student, absolutely stumped on this don't even know where to begin.

"Determine the vector potential due to an infinite cylinder of radius, R, carrying a uniform current
density, j. Use this to describe the magnetic field inside a current carrying wire

I am using this article
http://galileo.math.siu.edu/mikesullivan/Courses/251/S12/vpot.pdf

 

[rude man]

Unfortunately, in your link F is already given & they want you to find the vector potential of F.

In your problem on the other hand B is not given, it is to be derived from the vector potential: B = del x A where A is the vector potential.

There is an integral expression for finding A, given the current distribution and the location of the point where A and B are to be determined. What is it?

Warning: this looks to be a tough problem!

 

[haruspex]

In your problem on the other hand B is not given, it is to be derived from the vector potential: B = del x A where A is the vector potential.

That's not how I read the question. It does ask for the vector potential, so the cited paper could be useful. The missing part is that you need to compute the vector field first by some other means.

 

[rude man]

That's not how I read the question. It does ask for the vector potential, so the cited paper could be useful. The missing part is that you need to compute the vector field first by some other means.

I guess we just don't read the same way.

If you can cheat and get B first, which is a piece of cake here obviously, then what would be the point of describing the B field ex post facto using the vector potential?

 

[haruspex]

what would be the point of describing the B field ex post facto using the vector potential?

The question does not ask for that to be done. It asks us to find a vector potential (by whatever means).

 

[rude man]

The question does not ask for that to be done. It asks us to find a vector potential (by whatever means).

Yes, and then use it to describe the B field which you have already found? Ho ho ho.

I do have to admit, the problem as I read it is prohibitively difficult, so maybe it is just an exercise in redundancy.

 

[BeerScience]

Thanks for your help guys. I couldn't find an answers. Turns out heaps of guys in my class couldn't get it. Do you think this is too advanced for a second year physics degree?

 

[rude man]

Thanks for your help guys. I couldn't find an answers. Turns out heaps of guys in my class couldn't get it. Do you think this is too advanced for a second year physics degree?

Here's the thing. If haruspex is right and the only intent is to find the vector potential A with B already known, then you could solve the DE B = del x A, similar to what was in your link.

However, this is redundant nonsense. The reason A is solved for in the first place is to facilitate solving for B! And as I said, solving for A given the geometry and current density distribution is in this case horribly hard. I mean, very if not too hard even for an advanced e & m course. So to sum up I would say yes, this question is either pointless or impossible to solve.