Solving Biot-Savarts Law for Finite Thickness Current Loops

[Niles]

Hi

When solving Biot-Savarts law for a current loop of radius R, the magnetic field on the axis of the loop is given by (in Tesla)
$$B(z) = \mu_0I\frac{R^2}{(R^2+z^2)^{\frac{3}{2}}}$$
where I is the current through the loop. However, this derivation assumes that the loop has an infinitesimal thickness. But how is the "proper" way to take into account the fact that a current loops has a finite thickness?

My book on Electrodynamics (Griffiths) does not address this issue, and it is something I have thought about for some time.Niles.

 

[Dadface]

Hi

When solving Biot-Savarts law for a current loop of radius R, the magnetic field on the axis of the loop is given by (in Tesla)
$$B(z) = \mu_0I\frac{R^2}{(R^2+z^2)^{\frac{3}{2}}}$$
where I is the current through the loop. However, this derivation assumes that the loop has an infinitesimal thickness. But how is the "proper" way to take into account the fact that a current loops has a finite thickness?

My book on Electrodynamics (Griffiths) does not address this issue, and it is something I have thought about for some time.


Niles.

I suppose by carrying out a more sophisticated integration where,perhaps,the thick coil can be considered as a number of narrow coils connected side by side and making good electrical contact with each other.

(Is your equation missing a 2pi?)