I am considering the equivilence between Biot-Savart's Law and Ampere's Law for a current loop. The form of the magnetic field from a current element in the Biot-Savart law becomes(adsbygoogle = window.adsbygoogle || []).push({});

dB = [tex]\mu[/tex]_{o}I dL sin[tex]\theta[/tex]/4[tex]\pi[/tex]r^{2}

which in this case simplifies greatly because the angle =90 ° for all points along the path and the distance to the field point is constant. The integral becomes

B = [tex]\mu[/tex]_{o}I/2r

It would appear that there is sufficient symmetry to apply Ampere's Law, with the line integral

[tex]\oint[/tex] B dL cos [tex]\theta[/tex] = [tex]\mu[/tex]_{o}I

of the enclosed value B dL cos [tex]\theta[/tex] reflecting the surface area of a torus.

However, as I work this out I cannot get the same value as produced by Biot-Savart's Law.

Is the problem that the B Field is not constant such that the line integral

[tex]\oint[/tex] B dL cos [tex]\theta[/tex]

cannot be easily calculated?

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# Equivilence between Biot-Savart's Law and Ampere's Law

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