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Ampere's Law on Current Carrying Loop 
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#1
Oct613, 06:24 AM

P: 27

I haven't seen anyone derive the magnetic field density (B) using ampere's law, only using BiotSavart Law any reason why? if we cut the loop and loop at one end (of the new cut) and treat it as if it was a current carrying wire, then by ampere's law we'd get: B = u*I / 2*pi*r but however by the BiotSavart Law we actually get B = u*I / 2*r anyone know why? 


#2
Oct613, 08:24 AM

P: 2,195

Ampere's law tells you that (line integral of B.dl along the loop) = μ0 * (flux of I through the loop). If you know from the geometry of the situation that B is constant along the loop, then calculating the line integral of B along the loop is easy. This is the case with a long straight wire. Here we draw a loop at a distance R from the wire. We know from symmetry that the value of B is everywhere constant along the loop, so the line integral of B along the loop is just 2*pi*R*B. In the case of a current carrying ring, no matter how you draw your Amperian loop, there is no way to draw it so that B is constant. So, while Ampere's law still holds, it is not very useful, since you don't know how to calculate the line integral. So you use the BiotSavart law, which is more amenable to a general situation.



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