Understanding Magnetic Induction Field B on Circular Coil Axis

[retupmoc]

Just a quick question about finding the magnetic induction field B on the axis of a circular coil shown on page 7 on http://www.physics.gla.ac.uk/~dland/ELMAG305/Elmag305txt5.pdf
I understand why the field must be along the x-axis but why does (dlxr )x become dlrsin(alpha)? alpha doesn't seem to be the angle between the dl and r, dlxr would equal |dl|| r |sin(x) where x would be the angle between the dl and r. My problem is x and alpha don't seem to be the same angle so i don't know how to advance with this problem. Any help?

 

[dextercioby]

You can't denote the angle with "x",one of the axis with "Ox" and the sign for a vector/cross product with "x"...Let the angle be "alpha",the axis "Ox" and the sign $$\times$$.

Daniel.

 

[whozum]

I don't see why alpha wouldn't be that angle. What angle are you suggesting?

A is the radius of the circle, and r is the line drawn from the center of the loop at a distance x_i away. You are integrating I along every dl, during which the radius A rides along its resident circle once.

 

[dextercioby]

Oh,and it should be Biot-Savart-Laplace law...Laplace was the mathematician who made the formula up,while the other guys fooled around with magnets.

The same story with Stefan-Boltzmann law...Boltzmann was the theorist,and Stefan the experimentalist.

Daniel.