Derivation of the Biot-Savart law and calculating the magnetic field of a long straight wire.

00:00 We derive the Biot-Savart law from the magnetic field of a point charge formula, then we apply the Biot-Savart law to calculate the magnetic field of a long, straight wire.  Disclaimer:  this is a very common introduction to the Biot-Savart law in first year physics, but we should actually consider the Biot-Savart Law to be fundamental here as an experimental result.  The field of a point charge formula is actually a crude approximation of the low velocity limit of a formula obtained from far more sophisticated methods, and it's not really valid to use it as a basis for the derivation of the Biot-Savart law.  Regardless, this approach is intuitive, the derivation is a good review of several prior topics, and the whole thing probably makes sense as a teaching tool.  But be warned:  this is not the "real" answer, and you can't really get the real answer without going deep into upper division level electrodynamics!

01:13 Derivation of the Biot-Savart Law.

05:51 Calculating the magnetic field of a long straight wire.

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