Sources of Magnetic Field

This lecture is based on Serway, Sections 30.1 to 30.3. It covers some ways in which one can calculate the magnetic field created by a current running through a wire.

There are many similarities between the electric and magnetic fields -- you will see them here, and in future weeks.
Magnetic fields can be created by current moving through a conductor.
The Biot-Savart Law describes the magnetic field due to a tiny section of current, at some distance away from the wire.
One can integrate the Biot-Savart Law all the way across a wire in order to calculate the total magnetic field it generates. The integral may be complicated and difficult.
In a few situations with strong symmetry, one can use Ampere's Law to calculate the strength of a magnetic field created by current running through a conductor.
Ampere's Law relates the integral of magnetic field dotted with displacement around a loop to the amount of current running in wires which pass through the loop.
Ampere's Law is an analog (in two dimensions) to Gauss' Law (in three dimensions): both relate the properties of a field and a surface (or loop) to the amount of stuff within the surface (or loop).
One wire carrying a current creates a magnetic field; if there's another wire carrying a current nearby, the magnetic field will exert a force on it.
If two wires carry current in the same direction, the magnetic force pulls them together; if they carry current in opposite directions, the magnetic force pushes them apart.
The strength of the force between wires carrying current decreases as the inverse distance between them.

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