Download Magnetic Field of a Long Straight Wire

y
dB
P
r
r̂ 
ds
a

z
x
When L, B =
x
μ 0I
B=
2πa
1
4a2
1+ 2
L
I
μ 0I
.
2 πa
μ 0I
or B =
2 πr
The r in this equation has a different
meaning than the r in the diagram!
Magnetic Field of a Long Straight Wire
We’ve just derived the equation for the magnetic
field around a long, straight* wire…
μ0 I
B=
2 πr
I
B
r
…with a direction given by a “new” righthand rule.
link to image source
*Don’t use this equation unless you have a long, straight wire!
Looking “down” along the wire:
The magnetic field is not
constant (and not uniform).
I
B
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.
Homework Hints
The Biot-Savart law gives the magnetic field due to an
infinitesimal current-carrying wire:
μ 0 I d  rˆ
dB =
4π r 2
Integrate over the entire wire to get the total magnetic field. If
the wire is long and straight:
μ0 I
B=
2 πr
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.