Help involving vector (bio-savart law)

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The discussion centers on confusion regarding the application of the Biot-Savart law in calculating the magnetic field components for an exam. The user is struggling to understand why the textbook uses the integral \(\int dba/r\) instead of their approach of \(\int dbx/r\) for finding the x component of the magnetic field. A response clarifies that unlike electric fields, magnetic fields have loopy lines and the cosine factor must account for the perpendicular nature of the magnetic field to the radius vector. This distinction is crucial for correctly applying the Biot-Savart law in this context. Understanding this difference is essential for resolving the user's confusion before the exam.
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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?
 

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Anybody, please? It's a final and if I don't get this cleared up I'm going to be really confused :S
 
mmmboh said:
… 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! :smile:

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. :wink:
 

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