# Magnetig flux of a straight conductor

1. Feb 25, 2009

### Kruum

1. The problem statement, all variables and given/known data

http://www.aijaa.com/img/b/00815/3678868.jpg [Broken]

2. Relevant equations

$$B= \frac { \mu _0}{2 \pi r}I$$
$$d \phi = \vec{B} \cdot d \vec {A}$$

3. The attempt at a solution

I know the magnetic field of the conductor is $$B= \frac { \mu _0}{2 \pi r}I$$. And in order to solve the magnetic flux I need to integrate $$d \phi = \vec{B} \cdot d \vec {A}$$. But the question is, since the area is not square or rectangular, can I simply integrate over the whole area at once or do I need to cut the integral into pieces?

Last edited by a moderator: May 4, 2017
2. Feb 25, 2009

### LowlyPion

You will have different ranges along the wire that you will need to consider in the integral. Symmetry should make it easier to account for.

Let's consider this Introductory still?

3. Feb 25, 2009

### Kruum

So what your saying is, that I should divide the cross into three pieces and integrate them separately? So the first integral would be from r to r+b over the area of ab. The second from r+b to r+b+a over the area of (a+2b)a. And the third one from r+b+a to r+2b+a over the area of ab.

4. Feb 25, 2009

### LowlyPion

3 rectangles sounds good to me.

Slice them horizontally or vertically, which ever way your Ginsu slices the easiest.

5. Feb 25, 2009

Thank you!