Electromagnetism, Induction and Inductors
In the early 19th century a Danish physicist named Oerstad discovered that an electric current flowing in
a wire (a conductor) produced a magnetic field.
In specific it was also found that:
•
A DC current produces a constant magnetic field
•
An AC current produces a time-varying
magnetic field
Some Terminology
These terms all apply to a coil of wire through which a current flows.
Magnetic Flux (Φ)
One line of magnetic flux or force is referred to as a Maxwell. This unit is too small so a new unit of the
Weber = 108 Maxwells .
So Magnetic Flux (Φ) = number of lines of force or Maxwells given in Webers
Flux Density (B)
Flux density is the number of lines of force/unit area and is called the Tesla
Flux Density B = Φ/Area
Unit is Webers/m2 = Tesla (T)
Magnetomotive Force (mmf)
Magnetomotive Force (mmf) is the magnetic pressure that produces the magnetic field and is
equivalent to the electromotive force (voltage) that produces an electric field.
mmf = I x N (Amps-turns)
where I = the current in the wire
N = number of turns of wire
Magnetizing Force (H)
The Magnetizing Force describes the magnetic field strength.
H = (I x N)/L
where I = the current in the wire
N = number of turns of wire
L = Length of coil of wire
For a given coil where N and L are constant, the Magnetizing Force H is proportional to the current I.
Reluctance (R)
The reluctance is the opposition or resistance to the establishment of a magnetic field.
Reluctance (R) = mmf/Φ = magnetomotive Force/magnetic flux (Amp-turns/Weber)
This equation is analogous to that of Ohm’s Law. It can be seen that the magnetomotive force plays a
role in this equation analogous to the voltage V in Ohm's law: V = IR.
Permeability (µ)
The permeability is the ease with which a magnetic field can be established. Flux lines pass through
some materials easier than others. The ease of a material in passing flux lines is called permeability. Air
has a very low value of permeability.
Permeability (µ) = 1/ Reluctance (R)
The unit of permeability is Henrys/meter
If a material has a high permeability (low Reluctance) then a magnetic field can be easily established.
Permeability is equivalent to the quantity conductance in an electric circuit. Magnetic coils are usually
constructed around cores that are materials different from air.
The permeability of a material µ = µ0 x µr
where µ0 is the absolute permeability of air = 1.26 x 10-6 H/m
µr is the relative permeability of the core material
The table below shows some common values of relative Permeability - µr
Material
Relative Permeability - µr
air
1.0
Nickel
50
Cobalt
60
Cast iron
90
Transformer iron
5,500
Permalloy
100,000
The course web site shows a table of additional values. See the Relative
Permeability Learning Object on the course web site.
Faraday’s law
Faraday’s Law states that when there is relative motion between a conductor and a magnetic field, a
potential difference (voltage) is induced in the conductor.
Relative Motion can be established in 2 ways.
•
The conductor can be moved through a stationary magnetic field or a magnet can be moved
relative to a stationary conductor. If a load is connected to the conductor then a complete
circuit is established and an induced current will flow
•
A time-varying magnetic field can produces magnetic flux that interacts with a stationary
conductor
Self Inductance
If an AC voltage is connected to a coil of wire a current (in red) will flow in the coil. This current that
flows in the wire will (by Faraday’s law) induce another voltage (and current) in the wire. In the drawing
shown the direction of the induced current (in green) opposes the current that created it (Lenz’s law).
Lenz’s law
In the drawing below a magnetic is brought near the coil of wire. The flux lines of the magnet cut the
coil of wire and by nature of Faraday’s law a voltage (and a current) is induced in the coil of wire. Lenz’s
Law takes this 1 step further by saying that the induced current in the coil of wire produces a magnetic
field that opposes the magnetic field of the original magnet.
Inductance
In the circuit shown below, when the switch is closed current will flow through the resistor and inductor.
As the circuit has an AC source the current will start at zero and rise to its maximum and create an
expanding magnetic field. This varying magnetic field will, by nature of Faraday’s and Lenz’s Laws,
create an induced voltage (and current) that opposes the voltage that created it.
When the applied current reaches its maximum value the magnetic field is now constant and relative
motion between the magnetic field and the coil has dropped to zero as has the induced voltage in the
coil.
The current in the circuit (and the coil) now start to drop from the maximum value to zero, creating once
again relative motion between the magnetic field and the coil and an induced an induced voltage (and
current) that opposes the collapsing voltage that created it. Finally the action repeats itself when the
applied voltage increases again (with opposite polarity) producing a magnetic field with the magnetic
poles reversed and an induced voltage (and current) that opposes the voltage that created it.
This induced voltage is referred to as a counter emf or back emf as it opposes the applied voltage or emf
that produced it. This ability of a coil to produce a counter emf as a result of a changing current is called
the Self-Inductance or more simply the Inductance (L) of a coil or inductor and has the units of Henrys
(H).
The induced voltage can be determined as
Vinduced = - L ΔI/Δt
A coil with an Inductance of 1 Henry with a change in current of 1 Amp will have an
induced voltage of 1 V.
Construction of Inductors or Coils
An Inductor is just a length of insulated wire (so the turns of wire don’t electrically touch) wound on a
coil to enhance its magnetic properties. A drawing of the
construction of an inductor is shown.
The Inductance L of this coil or wire can be determined by its
physical properties.
L = ( µ0 x µr x N2 x A)/l
where
µ0 is the absolute permeability of air
µr is the relative permeability of the core
N is the number of turns of wire
A is the cross-section area of the coil
l is the length of the coil
Consult the web page Factors Affecting Inductance on the course web site
Inductors Ratings
Inductors are classified by their value of Inductance but Inductors like the other two basic components
have a secondary rating. An Inductor’s secondary rating is current. As a coil is made from wire, an
inductor with a larger diameter wire can handle a larger current without overheating.
Resistor
Capacitor
Inductors
Primary rating
Resistance - Ohms
Capacitance - Farads
Inductance - Henrys
Secondary rating
Power - Watts
Voltage - Volts
Current - Amps
Data Sheet Values
Source: http://www.murata.com/products/catalog/pdf/o05e.pdf
Inductor Faults
If the current through an Inductor exceeds the maximum value, the insulation covering the wire can be
melted causing turns of wire to touch and short out or if the heat is excessive the wire can actually melt
and break (like a fuse) and the inductor becomes an open circuit.
Inductors in Series
The total inductance of two inductors L1 and L2 that are connected in series is
LTotal = L1 + L2
For the circuit shown LTotal = 3 mH + 2 mH = 5 mH
In general if there are N inductors connected in series, the total inductance is
LTotal = L1 + L2 + L3 + … + LN
Inductors in Parallel
The total inductance of two inductors L1 and L2 that are connected in parallel is
LTotal = (L1 x L2)/(L1 + L2)
This expression has the same form as 2 resistors connected in parallel.
In the circuit shown the total Inductance LTotal = (6 mH x 4 mH)/(6 mH + 4 mH) = 2.4 mH
See the Inductors Learning Object on the course web site.