(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I know how to find the magnetic field at the center of a circular loop of wire carrying current. If the radius of the loop is R, how do you find the magnetic field at a distance a from the center of the loop where a<R?

2. Relevant equations

[tex]

d{\mathbf{B}} = \frac{{\mu _0 }}{{4\pi }}\frac{{Id{\mathbf{s}} \times {\mathbf{\hat r}}}}{{r^2 }}

[/tex]

3. The attempt at a solution

The small current element ds is always tangent to the loop. r varies from R-a to R+a. The angle θ between ds and [tex]\mathbf{\hat r}[/tex] seems to vary from 90° to some maximum angle that depends on a.

Also, if you define ϕ to be the angle around P from the place you first start to integrate to ds, then [tex]ds\neq rd\phi[/tex].

This is as far as I can analyze. I have no idea what to do with the angles. I am guessing there is some kind of relationship between r and θ or between r and ϕ or between θ and ϕ that I can't see.

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# Magnetic field of a circular loop of wire

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