Chapter 22: Electromagnetic Induction
• Induced emf and current
• Magnetic flux
• Faraday’s and Lenz’s laws
• Electric generators, back emf
• Omit 22.8, 22.9, (inductance and transformers)
Friday, February 3, 2006
1
Induced emf
When the magnet moves relative
to coil, a current is induced in the
coil.
Moving the coil to the magnet
produces the same deflection as
moving the magnet to the coil –
only the relative motion of coil
and magnet matters.
Reversing the magnet N and S
poles reverses the deflection.
Friday, February 3, 2006
2
Charges inside the moving rod experience a force
due to the magnetic field...
–––
++
+
I
!v
I
I
I
Conductor
The moving conductor acts as a generator.
The basis of electromagnetic induction.
Friday, February 3, 2006
3
Moving coil relative to field
Motion of coil
relative to
magnet
I
!v
!F
x
!B⊥
!B
!F !B
⊥
A charge Δq inside the wire moves with the coil relative to the magnetic
field. A component of field, B⊥, is perpendicular to the velocity of the coil.
The magnetic forces induce a current to flow around the coil.
Friday, February 3, 2006
4
Fm = Δq v B
Motional emf
The magnetic forces Fm separate +
and – charges in the conductor.
+Δq
Fq = Δq E
The separated + and – charges give
rise to an electric field E in the
conductor.
At equilibrium, the electrostatic force:
!E
Fq = Δq E
–Δq
balances the magnetic force.
That is:
Fm
Fq = Fm
E = vB
Also, E = V/L
So the induced potential difference between the ends of the rod is: V = vLB
22.4
Friday, February 3, 2006
5
Prob. 22.4: “Tethered Satellite Experiment”. A 20,000 m length of wire
is trailed behind the shuttle while in orbit around the earth. The orbital
speed of the shuttle is 7600 m/s.
If the earth’s magnetic field at the position of the shuttle is 5.1×10-5 T
and the wire moves perpendicular to the field, what is the induced emf
between the ends of the wire?
Wire
–
× !v
!B
+
V = vLB = 7600 × 20,000 × 5.1 × 10-5 = 7752 V
Negative at the top.
Friday, February 3, 2006
6
Prob. 22.2: The drawing shows a type of blood flow meter. Blood is
conductive enough that it can be treated as a moving conductor. When it
flows perpendicular to a magnetic field, electrodes can be used to measure
the small voltage that develops across the vessel.
Suppose the speed of the blood is 0.3 m/s, the diameter of the vessel is 5.6
mm and B = 0.6 T. What is the magnitude of the voltage that is measured?
!B
+++
L
–––
!v
Blood – a moving
conductor
Friday, February 3, 2006
7
Induced emf
The emf induced between the ends of a conductor that is moving in
a magnetic field is:
V = vLB
(V = vLB sin θ when the angle between !B and !v is θ)
The induced emf is the same whether the coil moves or the magnet
moves, only the relative motion matters.
Friday, February 3, 2006
8
Prob. 22.5: Each rod of length L = 1.3 m moves at speed v = 2.7 m/s in a
magnetic field, B = 0.45 T. Find the motional emf for each.
+
–
Friday, February 3, 2006
9
Prob. 22.C6: Initially the rod is at rest. Describe the rod’s motion after
the switch is closed. Be sure to account for the effect of any motional emf
that develops.
Friday, February 3, 2006
10
The rod experiences a magnetic force to the right and accelerates.
I
Friday, February 3, 2006
F
11
The rod is now moving in the magnetic field and generates its own emf
that opposes the emf of the battery (a “back emf”). The current therefore
decreases. The rod continues to accelerate until the current is reduced to
zero (assuming no friction).
+
v
I
–
Friday, February 3, 2006
12