Question about charged disk and current loop similarity

[bitrex]

I have a question regarding the similarity between the Biot-Savart law and the equation that gives the magnetic field inside a current loop, and the similar version of Coloumb's law that gives the electric field due to a charged ring. In the equation for a charged ring at http://hyperphysics.phy-astr.gsu.edu/Hbase/electric/elelin.html the equation is multiplied by the cosine of the angle between the point where the field is measured and the disk, however in the similar situation for a current carrying loop using Biot-Savart the equation is multiplied by the sine of the angle. See: http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/curloo.html#c2 My understanding of the difference is that in the case of the electric field the forces at the center of the disk are canceling by symmetry, hence when the angle is 90 degrees (at the center) the cosine is 0 and there is no force there. In the case of the current carrying wire, the magnetic field is strongest at the center of the loop and falls off with distance, so the sine of 90 degrees is 1 and decreases as the field is measured up the Z axis. I just want to make sure my understanding is correct - thanks for any help!

 

[kuruman]

The difference between the two cases is that the electric field element $d\vec E$ is along the line joining the charge element to the point on the axis whereas the magnetic field element $d\vec B$ is perpendicular to the line joining the charge element to the point on the axis. Thus, when you define the angle in a similar manner in the two cases, if you use the sine for the vertical component in one case, you have to use the cosine in the other.