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I have a question concerning Biot-Savart's law. It pertains to problems where you must find the total magnetic field at some point P, $x$ meters away from a current-carrying wire. I am a bit confused, because to my understanding, a current-carrying wire creates a magnetic field consisting of concentric circles. Now, when we use Biot-Savart's law, we take some current element $Idl$ and try to find its contribution to the overall magnetic field at point P. However, since every current element has a magnetic field consisting of concentric circles that line up evenly within the wire (that is to say, the circles are not tilted), then unless the current element that we are referring to is directly under point P, then it should not contribute anything to the magnetic field. Is there something that I'm missing here?

Is my question being understood or should I include some sort of a diagram to clarify?

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The incorrect part of your statements is that every current element does not have a circular magnetic field around it. Only an infinitely long wire would have perfectly circular magnetic field lines around it.

In fact every current element does contribute to the field at point P and has a component both perpendicular and parallel to the wire. However, for an infinite wire, the component of the B-field parallel to the wire contributed by any current element will be cancelled by a symmetrically placed element on the other side of point P. The components perpendicular to the wire do not cancel; they sum, but with a decreasing contribution from elements further from P.

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  • $\begingroup$ Ah, I see. I thought maybe that might be the case but every single illustration that I've seen has the magnetic fields on a current carrying wire represented by perfect circles perpendicular to the wire. Maybe they just illustrate it that way for simplicity. $\endgroup$ – French Toast Crunch Mar 26 '15 at 23:32
  • $\begingroup$ @FrenchToastCrunch Well for the field around a long wire it is approximately true. It is not true for a short wire element. $\endgroup$ – Rob Jeffries Mar 27 '15 at 7:52

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