Transcript Slide 1

Today’s agenda:
Magnetic Fields Due To A Moving Charged Particle.
You must be able to calculate the magnetic field due to a moving charged particle.
Biot-Savart Law: Magnetic Field due to a Current
Element.
You must be able to use the Biot-Savart Law to calculate the magnetic field of a currentcarrying conductor (for example: a long straight wire).
Force Between Current-Carrying Conductors.
You must be able to begin with starting equations and calculate forces between currentcarrying conductors.
Biot-Savart Law: magnetic field of a current element
From the equation for the magnetic field of a moving charged
particle, it is “easy” to show that a current I in a little length dl
of wire gives rise to a little bit of magnetic field.
r
dB
rˆ
dl
I
μ 0 I d  rˆ
dB =
4π r 2
The Biot-Savart Law
If you like to be more precise in your language, substitute
“an infinitesimal” for “a little length” and “a little bit of.”
I often use ds instead of dl because the script l does not
display very well.
You may see the equation written using r = r rˆ .
Applying the Biot-Savart Law
P
dB 
r

μ 0 I ds  rˆ
r
ˆ
dB =
where r =
2
4π r
r
ds  rˆ = ds rˆ sin 
= ds sin because rˆ =1
rˆ
ds
I
dB =
μ 0 I ds sin θ
4π
r2
B =  dB
Homework Hint: if you have a tiny piece of a wire, just calculate dB; no need to integrate.