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kbarry2295

- 3

- 0

## Homework Statement

Hello,

This is a multi-part problem but I am stuck on just the third part, but I am a little confused in general with Ampere's Law. I know that the equation is mu_0*Ienc=Integral of B dl, but this problem really confused me.

A long straight copper wire lies along the z axis and has a circular cross section of radius R. In addition, there is a circular hole of radius a running the length of the copper wire, parallel to the z axis. The center of thhe hole is located at x=b with a+b<R.

The first part was What is the current density J and the answer is that J=1/pi(R^2-a^2)

The second part said if the hole is not there but has the same current density J, which I was able to solve through Ampere's law and the answer is B=1/2 mu_0 J*r

Now the third part is where I have had troubles. It saws suppose the wire of radius R is not there, and in place of the hole there is a smaller circular wire of radius a, with center at x=b, carrying the same current density J but into the page. What would the magnetic field be on the x-axis at a distance b<r<a+b from the origin, inside the smaller wire?

## Homework Equations

Amperes Law

Integral of Bdl= current enclosed * mu_0[/B]

## The Attempt at a Solution

Alright, so my thoughts on this problem were to ignore the large copper wire loop like it said, and I drew a Ampere loop inside the smaller circle. On the left side of Ampere's law is B*2pir.

On the right hand side, Ienc= to the integral of Jda, but J is claimed to be the same so I can take that out of the integral, and then I just have the integral of da.

Now, I set up the integration to go from the middle of the small loop, which is B, to my Ampere Loop, which is R, to get a current enclosed of Jpi(r-b)^2 and I set that equal to the other side. But I am not getting the right answer which my textbook says it is B=0.5(mu_0)J(b-r). I am not really concerned with the direction at this point, more on where am I messing up in my thinking of Ampere's Law and why am I not getting to this same answer? Any help or suggestions is greatly appreciated!