Interaction of Magnetic Fields
(Motor Action)
• Look at adjacent current-carrying conductors
– Currents in opposite directions
– Flux “bunching” between the conductors
– Force of repulsion acts to separate the conductors
ECE 201 Circuit Theory I
1
Interaction of Magnetic Fields
(Motor Action)
– Currents in the same direction
– Flux in space between conductors in “opposite”
directions
– Force of attraction acts to pull the conductors together
ECE 201 Circuit Theory I
2
Elementary Two-Pole Motor
• Rotor core with 2 insulated conductors in “slots”
• A stationary magnet – the “stator”
ECE 201 Circuit Theory I
3
Current-Carrying Conductor
in a Magnetic Field
• Current-carrying conductor perpendicular to
the B-field
ECE 201 Circuit Theory I
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Magnitude of the force on the conductor
in a Magnetic Field
• Magnitude of the mechanical force on the conductor is
F  Bl
effective
I
Where F = mechanical force (N)
B = flux density in the stator field (T)
l
= the effective length of the rotor conductor
I = current in the rotor conductor (A)
effective
ECE 201 Circuit Theory I
5
Conductor “skewed” to the B-field
by angle 
l
= effective length of the rotor conductor (m)
l
 l(sin  )
effective
effective
leffective
leffective
l
 sin 
leffective  l sin 
ECE 201 Circuit Theory I
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Single-Loop Rotor Coil
Carrying a Current
Situated in a Two-Pole Field
ECE 201 Circuit Theory I
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Torque produced by the 2-conductor couple
T  2Bl
T  2Fd
D
D
ECE 201 Circuit Theory I
effective
Id
8
Elementary Two-Pole Generator
ECE 201 Circuit Theory I
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Voltage induced in the coil, e
• Flux through the coil
window is sinusoidal
• Φ = Φmaxsin(ωt)
•
•
•
•
•
•
Voltage induced in coil,e
e = N(dΦ/dt)
e = NωΦmaxcos(ωt)
Emax = ωNΦmax
Emax = 2πfNΦmax
Erms = 4.44fNΦmax
ECE 201 Circuit Theory I
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Directions of induced voltage and current
• Develop CCW countertorque
• “Bunching” must occur at
the top of coil side B and
the bottom of coil side A
• Coil current is CCW as
viewed from south pole
ECE 201 Circuit Theory I
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