Help involving vector (bio-savart law)

[mmmboh]

URGENT help involving vector (bio-savart law)

Hi, I have an exam monday and normally have no problems finding the components of integration, however in this one I don't know why but I do. Current is flowing in the loop in the direction shown, and a is the radius of the loop. The magnetic field from the y-components cancel out, so all that there is is the x component. To find the x component I thought it is $$\int$$ dbx/r...but according to my textbook and an old exam it is $$\int$$ dba/r...I have been trying to figure out the logic behind this but I cannot figure it out, we did a problem like this in class and the teacher did it my way....can someone help please?

 

[mmmboh]

Anybody, please? It's a final and if I don't get this cleared up I'm gonna be really confused :S

 

[tiny-tim]

… To find the x component I thought it is $$\int$$ dbx/r...but according to my textbook and an old exam it is $$\int$$ dba/r...

Hi mmmboh!

If it was an electric field, the field lines would go straight out, and E would be along r, so you would get the x-component by multiplying by x/r.

But the magnetic field has loopy field lines, and B is perpendicular to r, so the cosine is of the complementary angle, and is a/r.