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Electromagnetic Induction
What do we know?
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Hans Christian Oersted showed that moving
charges create a magnetic field.
Forces in Magnetism
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The existence of magnetic fields is known
because of their affects on moving charges.
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What is magnetic force (FB)?
How does it differ from electric force (FE)?
What is known about the forces acting on
charged bodies in motion through a magnetic
field?
• Magnitude of the force is proportional to the
component of the charge’s velocity that is
perpendicular to the magnetic field.
• Direction of the force is perpendicular to the
component of the charge’s velocity
perpendicular to the magnetic field(B).
Magnetic Force (Lorentz Force)
FB = |q|vB sinθ
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Because the magnetic force is always
perpendicular to the component of the
charge’s velocity perpendicular to the
magnetic field, it cannot change its speed.
Force is maximum when the charge is
moving perpendicular to the magnetic
field ( = 90).
The force is zero if the charge’s velocity is
in the same direction as the magnetic field
( = 0).
Also, if the speed is not changing, KE will
be constant as well.
What is the magnetic field (B)?
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The magnetic field is a force field just like electric and
gravitational fields.
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It is a vector quantity.
Hence, it has both magnitude and direction.
Magnetic fields are similar to electric fields in that the field
intensity is directly proportional to the force and inversely
related to the charge.
E = FE/q
B = FB/(|q|v)
Units for B: N•s/C•m = 1 Tesla
Example 2: Lorentz Force
Two protons are launched into a magnetic field with the same
speed as shown. What is the difference in magnitude of the
magnetic force on each particle?
a. F1 < F2
b. F1 = F2
c. F1 > F2
F = qv x B = qvBsinθ
Since the angle between B and the
particles is 90o in both cases, F1 = F2.
+
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How does the kinetic energy change once the particle is in the
B field?
a. Increase
b. Decrease
c. Stays the Same
Since the magnetic force is always perpendicular to the
velocity, it cannot do any work and change its KE.
Faraday’s Hypothesis
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If moving charges produced a
magnetic field, could a moving or
changing magnetic field produce a
current?
Key Ideas
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Lorentz Force: A charge moving perpendicular to
a magnetic field will experience a force.
Charged particles moving perpendicular to a
magnetic field will travel in a circular orbit.
The magnetic force does not change the kinetic
energy of a moving charged particle – only
direction.
The magnetic field (B) is a vector quantity with
the unit of Tesla
Use right hand rules to determine the
relationship between the magnetic field, the
velocity of a positively charged particle and the
resulting force it experiences.
Faraday’s Discovery
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Faraday discovered that he could induce
current by moving a wire loop through a
magnetic field or moving the magnetic field
through a wire loop.
Faraday’s Discovery is known as
Electromagnetic Induction
Faraday's Discovery
Electromotive Force
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Last week we learned the Lorentz Force.
FB = qvB sinθ = BIL sinθ
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When a conductor moves through a magnetic
field, a force is exerted on these charges causing
them to separate, inducing an EMF. Which end
of the wire is positive?
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Electromotive Force
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Last week we learned the Lorentz Force.
FB = qvB sinθ = BIL sinθ
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When a conductor moves through a magnetic
field, a force is exerted on these charges causing
them to separate, inducing an EMF.
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Electromotive Force
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The EMF results when the conductor has a velocity
component perpendicular to the magnetic field.
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Use RHR #1 where the thumb points in the direction of the
velocity. The force on the bar is opposite the velocity.
Example 1: EM Induction
A segment of a wire loop is moving downward
through the poles of a magnet, as shown. What
is the direction of the induced current?
a. The current direction is out-of the page to the left.
b. There is no induced current.
c. The current direction is into the page to the right.
Example 2: EM Induction
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The drawing shows three identical rods (A, B, and C)
moving in different planes in a constant magnetic field
directed along the +y axis. The length of each rod and the
speeds are the same, vA = vB = vC. Which end (1 or 2) of
each rod is positive?
Rod A:
a. 1
b. 2
c. neither
b. 2
c. neither
b. 2
c. neither
Rod B:
a. 1
Rod C:
a. 1
Magnetic Flux
What is magnetic flux?
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Like electric flux
A measure of the strength of the magnetic field, B,
passing through a surface perpendicular to the field.
For a bar magnet, the flux is maximum at the poles.
The more magnetic field lines, the higher the flux.
=BAcos
Magnetic Flux and EMF
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We already know:
EMF = vBL
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v = Δx/Δt = (x – xo)
(t – to)
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EMF = (Δx/Δt)BL = (xL – xoL) B = (BA) – (BAo)
(t – to)
(t – to)
EMF = -ΔΦ/Δt Where:
 = BA cos and
 = the angle the normal
to the surface makes
with B (in this drawing it
is 0o).
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Faraday’s Law of EM Induction
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In the drawing on the previous slide, there is
only one loop in the circuit.
When there is more than one loop in a circuit, as
in the coil of a solenoid, the EMF induced by a
changing magnetic field will increase by a factor
equal to the number of loops in the coil.
EMF = -N ΔΦ/Δt
Where N = the number of loops in the coil.
Lenz’s Law Per 6 & 7
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The induced EMF resulting from a changing
magnetic flux has a polarity that leads to an
induced current whose direction is such that
the induced magnetic field opposes the original
flux change.
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If the magnetic field is increasing, a current will
develop to oppose the increasing magnetic field.
If the magnetic field is decreasing, a current will
develop to create a magnetic field in the same
direction as the one that is decreasing.
A current will form that attempts to keep the
magnetic field constant.
Lenz’s Law abides by the laws of conservation of
energy.
Lenz’s Law
Lenz's Law
Lenz’s Law
Current will be
induced in the
copper ring when
it passes through
a region where
the magnetic field
changes. When
the magnetic field
is constant or
absent, their will
be no induced
current.
No Current
Induced
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Current
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No Current
No Current
Applications of Lenz’s Law
(Eddy Currents)
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Eddy current balances.
Eddy current dynamometer.
Metal detectors (Lenz's Law)
Braking systems on trains.
What are Eddy currents?
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Eddy currents are currents created in conductors to
oppose the changing magnetic fields they are exposed
to.
Eddy currents respond to the changes in an external
magnetic field.
Eddy currents can form in conductors even if they are
not capable of being magnetized.