In the Biot Savart law, it's my understanding that dL represents an infinitesimally small length of the wire carrying current. See below.

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However, I ran into a practice problem that is confusing me. I've pasted it below. In this problem, instead of using length of the wire for dL, they use the diameter of the wire. Why? I thought you use length?

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This problem is confusing and poorly worded. It might be better if it came with a diagram. I definitely was confused at first too.

The problem is asking for the "infinitesimal" magnetic field (note they write the final answer as $dB=...$ instead of $B=...$) at the center of this configuration contributed from a 1.22 mm length of wire located at the midpoint of each wire. So then $dl=1.22\space mm$ is the length of this "infinetesimal" wire segment. It is not saying the diameter of the wire is 1.2 mm. The wire is still assumed to be infinitely thin.

The problem is not asking about the field produced from the entire configuration, just the field made by those four specific points on the configuration. It would be like taking an shell with charge on it and saying "What is the electric field at the center of the shell from just four charges on the outside of the shell?"


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