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I was reading Purcell's book (see page 209, figure 6.6a : http://books.google.com.ar/books?id...resnum=1&ved=0CAoQ6AEwAA#v=onepage&q=&f=false) and I fell over an exercise I had done previously, but he says that the curvilinear integral is null because BC and DA are perpendicular to B and they contribute to nothing. (I understand that they don't contribute to the B field thanks to Biot-Savart law, because [tex]d\vec l[/tex] and [tex]\vec r[/tex] are parallel, so the cross product is null. But from his argument I don't understand at all since CD and AB are also orthogonal to B!!!!).

However he also says that AB cancels out CD, hence the total integral is null. That was what my intuition believed before I solved the exercise.

Precisely, I get that [tex]\vec B = \frac{\mu _0 I}{4\pi r_1}-\frac{\mu _0 I}{4 \pi r_2} \hat k[/tex]. And because [tex]r_2>r_1[/tex], the magnetic field is not null.

Notice that I took [tex]\hat k[/tex] pointing into the sheet of paper.

I'd appreciate very much if someone could point me if I did wrong the exercise and explain better the situation. (I don't see how Purcell's argument holds, but he's a Nobel prize and I'm just a second year student).

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# Homework Help: Magnetic field problem

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