Download 1. Magnetic field due to a current a differential current

PLAN
1. Magnetic field due to a current
♣ a differential current-length element
♣ i in a long straight wire
♣ i in a circular arc of wire
2. Force between two parallel currents
Electricity vs Magnetism
Electricity
Magnetism
The one law
No “magnetic charges”
(monopoles) have been found.
Coulomb’s law Ù Gauss’ law
•
•
About the force between two
point charges. (Dependence of the
electric field on the source charge
and distance.)
Alternatively, about the property of
the electric field.
Everything else is derived from this
law, which completely agrees with all
observed electrical phenomena.
The equation about the force
between two small bar magnets
turns out to be not fundamental.
What are fundamental?
1. Dependence of the magnetic
field on the strength of the
source (a current) and distance.
Chapter 29
2. The force due to a magnetic
field. The force on what?
Chapter 28
Magnetic field due to a differential current-length element
µ 0 i ds sinθ
dB =
4π
r2
µ 0 = 4π × 10 −7
Tm
A
"k *"=
µ0
Tm
= 10 −7
4π
A
• Why does “k*” have such a simple value?
Magnetism is inseparable from electricity. Magnetism
and electricity together require only one “ugly” constant
ε0.
• What is the purpose of 4π in the denominator?
To simplify an equivalent law which involves a
integral (Ampere’s law).
Field produced by brain activities
• Imaging brains
X-ray tomography (CAT scan); NMR imaging (MRI)
• Diagnosis of brain functions
Electroencephalography (EEG) --- the brain as a black
box; positron emission tomography (PET scan);
magnetoencephalography (MEG)
CHECKPOINT 1
The three circuits carry the same current.
Q1 Which circuit produces the strongest
magnetic field at the center marked by the
dot?
a
Q2 Which circuit produces the weakest field
at the center? b
CHECKPOINT 2
OUT
OUT
IN
The three long parallel wires, equally spaced,
carry the same current.
Q1 Which wire receives the strongest force
due to the currents in the other two ? b
Q2 Which wire receives the weakest force?
a