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Chapter 22
Electromagnetic Induction
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1) Induced emf and induced current
• Changing B-field induces current
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• Changing coil area or orientation induces current
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• Changing the number of lines of force through loop induces current
• Induced current indicates induced emf and induced electric field
• Changing magnetic field produces electric field
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2) Motional emf
a) The principle
• B-field exerts force on moving charges
€
FB = qvB
+v
FB -v
FB
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==> free charges separate
EE
€
E =E / L
• separated charges produce electric field and a corresponding potential difference
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EE
• E - field exerts force on charges
+
FE -
FE
€
FE = qE
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EE
• Charges stop moving when the forces balance:
€
qvB = qE
€
vB =E /L
Induced emf predicted from statics
€
E =vBL
so,
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2) Motional emf
b) Application
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c) Induced emf from conservation of energy
FA= FB
FB
€
FB = ILB
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FA= FB
FB
€
P =ΔW
Δt
Power to push rod at speed v:
€
P =E (vBL)
R
€
F = ILB and I =E /RUsing,
€
=Δ(FA x)
Δt
€
=FΔx
Δt
€
=Fv
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FA= FB
FB
Power to push rod at speed v:
€
P =E (vBL)
R
Electrical power consumed:
€
P =E 2
R
So,
€
E =vBL
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3) Magnetic flux,
a) Define Flux:- Proportional to the lines of force through a surface
B
Normal
€
∝| B |
Φ∝ A (area)
Φ∝ cosφ
€
=BAcosφ
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b) Flux and motional emf
t
€
E =vBL
€
=Δx
ΔtBL
€
=ΔA
ΔtB
€
=ΔΔt
€
E =ΔΔt
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4) Lenz’s law
Direction of induced current produces a magnetic field that opposes the change in flux
-flux into loop increases because of v: ΔΔt > 0
- induced current produces flux out of loop (opposite direction)
-Define external flux as positive. Then
€
E =−ΔΔt
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-flux into loop decreases because of v: ΔΔt < 0
- induced current produces flux into loop (same direction to oppose the decrease)
-Define external flux as positive. Then induced flux is also positive, so again
€
E =−ΔΔt
v
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5) Faraday’s Law
For any changing flux in any loop, the emf induced in the loop is (for N turns)
€
E =−ΔΔt
N
where is the flux through one turn
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7) Induction and sound
• Microphone
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• Guitar pickup
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• Magnetic tape