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?