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Biot-Savarts law

by Niles
Tags: biotsavarts
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Niles
#1
Feb11-12, 05:41 AM
P: 1,863
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)
[tex]
B(z) = \mu_0I\frac{R^2}{(R^2+z^2)^{\frac{3}{2}}}
[/tex]
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.

Best,
Niles.
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Dadface
#2
Feb11-12, 10:09 AM
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P: 2,031
Quote Quote by Niles View Post
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)
[tex]
B(z) = \mu_0I\frac{R^2}{(R^2+z^2)^{\frac{3}{2}}}
[/tex]
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.

Best,
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 eachother.

(Is your equation missing a 2pi?)


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