Biot-Savart current loop equation confusion?

[neg_ion13]

Hello,

I am having a bit of a problem with this classic example. I know about the symmetry but I would like to push through the math anyway. The field point is at distance Z from loop on Z axis. Using cylindrical coordinates I am at:

dH = I*(rho)d(phi)*a(phi) X (z*az - rho*a(rho)) / 4*pi*((rho)^2 + z^2))(3/2)

I know H(rho) doesn't contribute to total H. If I remove rho*a(rho) I have a cross product of az and a(phi) which is a(rho). I don't want to just jump to the numerator being i*(rho)^2*az or use trig substitutions so where is my mistake?

 

[berkeman]

Hello,

I am having a bit of a problem with this classic example. I know about the symmetry but I would like to push through the math anyway. The field point is at distance Z from loop on Z axis. Using cylindrical coordinates I am at:

dH = I*(rho)d(phi)*a(phi) X (z*az - rho*a(rho)) / 4*pi*((rho)^2 + z^2))(3/2)

I know H(rho) doesn't contribute to total H. If I remove rho*a(rho) I have a cross product of az and a(phi) which is a(rho). I don't want to just jump to the numerator being i*(rho)^2*az or use trig substitutions so where is my mistake?

Could you perhaps post a sketch of the geometry? I think I understand what you are asking, but I'm not sure.

http://en.wikipedia.org/wiki/Biot-savart

Also, if you can use Latex to post the equations, it makes it much more readable. There's a toturial on how to post using Latex in the Math & Science Learning Materials forum stickied at the top:

https://www.physicsforums.com/showthread.php?t=8997

Or when you post in the Advanced Reply window, there is an equation editor button that looks like a capital sigma near the right of the tool buttons.