Electromagnetic Induction

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Electromagnetic Induction
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What do we know?

• Hans Christian Oersted showed that moving charges
  create a magnetic field.

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Forces in Magnetism

• The existence of magnetic fields is known because
  of their affects on moving charges.
• 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 charges velocity that is
  perpendicular to the magnetic field.
• Direction of the force is perpendicular to the
  component of the charges velocity perpendicular
  to the magnetic field(B).

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Magnetic Force (Lorentz Force)

• FB qvB sin?
• Because the magnetic force is always
  perpendicular to the component of the charges
  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 charges velocity is in
  the same direction as the magnetic field (?
  0?).
• Also, if the speed is not changing, KE will be
  constant as well.

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What is the magnetic field (B)?

• The magnetic field is a force field just like
  electric and gravitational fields.
• 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/(qv)
• Units for B Ns/Cm 1 Tesla

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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 lt F2 b. F1 F2 c.
F1 gt F2
F qv x B qvBsin? Since the angle between B
and the particles is 90o in both cases, F1 F2.
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.
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Faradays Hypothesis

• If moving charges produced a magnetic field,
  could a moving or changing magnetic field produce
  a current?

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Key Ideas

• 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.

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Faradays Discovery

• 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.
• Faradays Discovery is known as Electromagnetic
  Induction
• Faraday's Discovery

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Electromotive Force

• Last week we learned the Lorentz Force.
• FB qvB sin? BIL sin?
• 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

• Last week we learned the Lorentz Force.
• FB qvB sin? BIL sin?
• 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

• The EMF results when the conductor has a velocity
  component perpendicular to the magnetic field.
• Use RHR 1 where the thumb points in the
  direction of the velocity. The force on the bar
  is opposite the velocity.

I
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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.

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Example 2 EM Induction

• 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
• 1 b. 2 c. neither
• Rod B
• 1 b. 2 c. neither
• Rod C
• 1 b. 2 c. neither

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Magnetic Flux

• What is magnetic flux?
• 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?

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Magnetic Flux and EMF

• We already know
• EMF vBL
• v ?x/?t (x xo)
• (t to)
• EMF (?x/?t)BL (xL xoL) B (BA) (BAo)
• (t to) (t to)
• EMF -?F/?t Where
• ? BA cos? and
• the angle the normal
• to the surface makes
• with B (in this drawing it
• is 0o).

I

x x x x x x x x x
x x x x x x x x x x
x x x x x
F
I
v
-
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Faradays Law of EM Induction

• 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 ?F/?t
• Where N the number of loops in the coil.

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Lenzs Law Per 6 7

• 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.
• 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.
• Lenzs Law abides by the laws of conservation of
  energy.

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Lenzs Law
Lenz's Law
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Lenzs 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.

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Applications of Lenzs Law (Eddy Currents)

• Eddy current balances.
• Eddy current dynamometer.
• Metal detectors (Lenz's Law)
• Braking systems on trains.
• What are Eddy currents?
• 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.