1. y P  dB r a  x  z ds I x When L, or
The r in this equation has a different meaning than the r in the diagram!

2. *Don’t use this equation unless you have a long, straight wire!
Magnetic Field of a Long Straight Wire
We’ve just derived the equation for the magnetic field around a long, straight* wire… I B r
…with a direction given by a “new” right-hand rule.
link to image source
*Don’t use this equation unless you have a long, straight wire!

3. Looking “down” along the wire:B  I
The magnetic field is not constant (and not uniform).
At a fixed distance r from the wire, the magnitude of the magnetic field is constant (but the vector magnetic field is not uniform).
The magnetic field direction is always tangent to the imaginary circles drawn around the wire, and perpendicular to the radius “connecting” the wire and the point where the field is being calculated.

4. Homework Hints
The Biot-Savart law gives the magnetic field due to an infinitesimal current-carrying wire:
Integrate over the entire wire to get the total magnetic field. If the wire is long and straight:
If you want to calculate the field of a tiny segment of a wire (“tiny”= wire segment length is much less than other lengths/distances in the problem) you can use the Biot-Savart law directly. No need to integrate.