Self Induction
The magnetic field generated by a d (n B )
coil also induces an emf in itself. V =−
This voltage is given by: dt
Note that the voltage is only induced for a changing flux.
n B = Li
The number in parenthesis is called the flux
linkage, and is proportional to the current in
the coil.
The constant of proportionality is labeled the inductance, L.
d (n B ) di
V= = −L
dt dt
Most induction sensors measure the change in L; e.g. as a result of
motion.
V
L=−
di
dt
We can therefore define the inductance
Induction notes
The defining V
equation is:
L=−
di
dt
Induced voltage is proportional to current change
Voltage is zero for DC (inductors look like short circuit to DC)
Voltage increases linearly with rate of change of coil current
Voltage polarity different for increased and decreased current in
same direction
Induced Voltage in direction which acts to oppose change in
current
Calculating inductance
Inductance can be calculated from geometry
n B
For a closely packed coil it is L=
i
N B = (nl ) ( BA)
If n is the number of turns per unit
length, the number of flux
linkages in a length l is
N B
Plugging in the expression B
for a solenoid gives:
L= = 0 n lA
2
Note that lA is the volume of the solenoid, so keeping n constant
and changing the geometry changes L
Inductors and complex resistance
In an electronic circuit, inductance can
V
be represented as complex resistance,
like capacitance.
= jL
i
i(t) is a sinusoidal current having a frequency =2f
Two coils brought near each
other one coil induces an emf in di1
V2 = − M 21
the other dt
Where M21 is the coefficient of mutual inductance between
the coils.
Mutual inductance.
For a coil placed around
a long cylinder: M = 0R nN 2
0 N1 N 2 h b
For a coil placed around a torus, M= ln( )
mutual inductance is 2 a
Example: Magnetic Motion Sensor
Pickup coil with N turns, moves into the gap of a permanent magnet
Flux enclosed by the loop is: b = Blx
The induced d B d dx
V =− = − N ( BLx) = −nBl = nBlv
voltage is: dt dt dt
Magnetic Resonance Imaging (MRI)
MRI uses the hydrogen atom
➢ 1 electron orbits the nucleus
➢ The nucleus contains no neutrons but contains 1 proton
The hydrogen nucleus has a net positive charge
➢ Hydrogen nucleus is a spinning, positively charged particle
Why hydrogen?
➢ Very abundant in the human body-H2O
➢ Has a large magnetic moment
Law of Electromagnetism
➢ A charged particle in motion will create a magnetic field
➢ The positively charged, spinning hydrogen nucleus generates a
magnetic field
MR Active Nuclei
odd # protons
or
odd # neutrons
or
BOTH
e.g. Hydrogen1, Carbon13, Nitrogen15, Oxygen17, Fluorine19,
Sodium23, Phosphorus31
