Magnetism

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Magnetism

• Magnetism
• Permanent and Temporary
• See FSUs site for much more information!!
• http//micro.magnet.fsu.edu/electromag/index.html
• 1

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Magnetic Topics

• Magnetism, B
• Electromagnetic Induction

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Assignments

• Read and write reflections on Ch 3637 in
  Conceptual Physics
• Complete Summaries for 3637

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General Properties of Magnets

• Like magnetic poles repel unlike magnetic poles
  attract
• Magnetic field lines are directed from north to
  south
• Magnetic field lines always form close loops
  http//www.walter-fendt.de/ph11e/mfbar.htm
• A magnetic field exists around any wire that
  carries current

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Genl Properties cont.

• Spinning electrons are small magnets.
• A current-carrying wire experiences a force when
  the wire is perpendicular to a magnetic field. A
  coil of wire that carries a current has a
  magnetic field about a permanent magnet
• http//micro.magnet.fsu.edu/electromag/java/farada
  y/index.html

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Magnetic Facts

• The source of all magnetism is moving electric
  charges.
• Surrounding every moving electron is both an
  electric field and a magnetic field.
• Even in a broken magnet, there is N and S.
• A small compass in a magnetic field will line up
  parallel with the magnetic field lines.
• Magnetic domains are regions of aligned atoms.
• Magnets can attract unmagnetized objects by
  temporarily producing magnetism in the object.
• Magnetic fields are always produced by current
  carrying wires.

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• The magnetic pole in the N Hemisphere is in
  Canada.
• The Earths magnetic field is probably due to
  convection currents in Earths molten interior.
• Magnetic deflection is the discrepancy between
  magnetic and true norths.
• The greatest force on an electron moving in a
  magnetic field is when the angle of motion is
  90o.
• Cosmic rays are most intense at Earths poles
  producing aurorae.
• Earths geographic South pole is nearest its N
  pole.
• Electric fields can increase a moving electrons
  speed.

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• A magnetic force field can accelerate an electron
  by changing its direction, not its speed.
• If a current carrying wire in magnetic field is
  caused to move down, current flowing in the
  opposite direction will cause the wire to move up.

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Forces Caused by Magnetic Fields

• When a current-carrying wire is placed in a
  magnetic field, a force acts on the wire that is
  perpendicular to both the field and the wire.
  Meters operate on this principle.
• Magnetic field strength is measured in tesla, T
  (one newton per ampere per meter).
• b is the symbol for magnetic field

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Forces cont.

• An electric motor consists of a coil of wire
  (armature) placed in a magnetic field. When
  current flows in the coil, the coil rotates as a
  result of the force on the wire in the magnetic
  field.

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Forces cont.

• The force a magnetic field exerts on a charged
  particle depends on the velocity and charge of
  the particle and the strength of the magnetic
  field. The direction of the force is
  perpendicular to both the field and particles
  velocity.

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Key Equations

• F BIL ? Force on a current carrying wire in a
  magnetic field. Force magnetic field strength
  x current x length of wire. Newton tesla x amp
  x meter
• F BqV ? Force of a magnetic field on a single
  charged particle. Force magnetic field
  strength x charge x velocity of the charge.
  Newton tesla x coulomb x m/s

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• E - N DF / D t
• Amperes Rule for parallel, straight conductors
  F 2k l I1 I2 / d
• Transformer Equations
• Pp Ps ? VpIp VsIs
• Is Vp Np
• Ip Vs Ns
• Induction
• M -Es / D Ip/ D t
• L -E / D I / D t

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The small picture how magnetism occurs

• Domain theory when enough atoms of a substance
  line up in the same direction
• Strong magnets iron and steel
• Very strong Alnico alloy
• Weak aluminum, platinum
• Natural magnetite or lodestodes formed when
  rock was molten

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Magnetic field lines

• Magnetic flux, (F) number of field lines
  passing through a surface
• Unit weber 1 nm/amp
• Magnetic flux density, B F /A
• Unit wb/m2 nm/a m2 n/am
• 1 wb/m2 1 Tesla
• Earth, 104 T Humans, 1011 T

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Hand Rule 1- B field direction around a current
carrying wire

• Point thumb in direction of current in the wire
• Fingers of your hand circle the wire and show the
  direction of the magnetic field
• Knuckles, N
• Finger tips, S
• http//www.walter-fendt.de/ph11e/mfwire.htm

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Hand Rule 2 Determine the polarity of an
electromagnet

• Wrap the fingers of your right hand around the
  loops in the direction of the current
• Extended thumb points toward the N pole of the
  electromagnet

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Solenoid conducting linear coil which acts like
a bar magnet

• Increase B, magnetic flux density by
• Increasing the current
• Adding loops of wire
• Inserting an iron core into solenoid now it is
  an electromagnet

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Hand rule 3 shows force acting on wire in B
field

• Lay right hand flat, palm up
• Extend thumb 90 degrees to rest of fingers
• Fingers point in direction of B field
• Thumb points in direction of current, I
• Imaginary vector coming up perpendicular out of
  the palm points in the direction of force acting
  on current carrying wire.

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Fingers point in direction of b field Thumb -
direction of current flow Imaginary vector
coming from palm is direction that conductor is
forced out of the field
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Sample Problems

• A straight wire that carries a 5.0 amp current is
  in a uniform magnetic field oriented at right
  angles to the wire. When 0.10 m of the wire is
  in the field, the force on the wire is 0.20 n.
  What is the strength of the magnetic field, B?

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Solution

• Known Unknown
• I 5.0 amp B ?
• L 0.10m
• F 0.20 N
• FBIL ? B F/IL
• 0.20N/5.0 amp(0.10m)
• 0.40 T

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Sample Problem

• A beam of electrons travels at 3.0 x 106 m/s
  through a uniform magnetic field of 4.0 x 101 T
  at right angles to the field. How strong is the
  force that acts on each electron?
• Known Unknown
• V 3.0 x 106 m/s F ?
• B 4.0 x 101 T
• Q - 1.6 x 1019 c

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Solution

• F BqV
• 4.0 x 101 T (-1.6 x 1019c)(3.0 x 106 m/s)
• -1.9 x 1013 Tcm/s
• -1.9 x 10 -13 n

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Moving Charges in a Magnetic Field
Right-Hand Rule for Moving Charges      
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Sources

• http//www.walter-fendt.de/ph11e/electricmotor.htm
  
• http//www.walter-fendt.de/ph11e/lorentzforce.htm
• Other physics information http//www.walter-fendt
  .de/ph11e/
• Great diagrams of magnetic rules
  http//sol.sci.uop.edu/jfalward/magneticforcesfie
  lds/magneticforcesfields.html

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Electromagnetic Induction (EMI)

• Relative motion between a conductor and a
  magnetic produces both current and a magnetic
  field
• Electric current can be induced in a wire by
  moving a magnet up and down near the wire
• More loops in a coil of wire (solenoid) increases
  the voltage produced
• Placing an iron rod in a current-carrying wire,
  yields a greater magnetic field

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• A generator changes mechanical energy to
  electrical energy. A motor does opposite
• An e-m wave contains perpendicular electric and
  magnetic fields
• E-M waves travel at the speed of light

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Michael Faraday and Joseph Henry around the same
time

• Discovered that when there is relative motion
  between a magnetic field and a complete circuit
  (and the conductor cuts across the magnetic
  field), that electricity will flow!!! An induced
  EMF causes electricity to flow.

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If current flows, there must be an EMF this is
EM induction

• Faradays Law of Induction
• E - N DF / D t
• E, emf, volts
• -N, of turns of wire (- means the current
  opposes the change that induced it)
• DF, change in flux in weber, wb
• t, change in time, sec
• This essentially says that the induced voltage in
  a coil is proportional to the product of the
  number of loops and the rate at which the
  magnetic field changes within those loops.

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Sample Problem

• If a coil of 200 turns is moved perpendicularly
  in a magnetic field at a constant rate, find the
  induced emf. The flux linkage change ( DF / D t)
  
• is 4.00 x 10-6 wb in 0.0100 sec.

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If a coil of 200 turns is moved perpendicularly
in a magnetic field at a constant rate, find the
induced emf. The flux linkage change ( DF / D t)
is 4.00 x 10-6 wb in 0.0100 sec.

• E - N DF
• D t
• E (-200)(4.00 x 10 6 wb)
• 1.00 x 10 2 s
• E -8.00 x 10 2 v
• Imagine what thousands of turns would produce!

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Electric Generators

• Convert mechanical energy into electrical energy
  by rotating a looped conductor (armature) in a
  magnetic field
• Alternating-Current electricity produced is
  conducted by slip rings and brushes to be
  used
• Direct current can be produced by using split
  rings

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A coil with a wire is wound around a 2.0 m2
hollow tube 35 times. A uniform magnetic field is
applied perpendicular to the plane of the coil.
If the field changes uniformly from 0.00 T to
0.55 T in 0.85 s, what is the induced emf in the
coil?
A 2.0 m2 N 35 B .55 T Dt 0.85 s E -N
D F / D t - NBA / D t E 35 (0.55 T) (2 m 2)
0.85s E 45.3 v
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Generator Output
Rectifier changes AC to DC Inverter changes DC
to AC
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Lenzs Law -

• The direction of an induced current is such that
  the magnetic field resulting from the induced
  current opposes the change in he field that
  caused the induced current.
• When the N pole of a magnet is moved toward the
  left end of a coil, that end of the coil must
  become a N, causing induced current flow in
  opposition.

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Inductance

• The property of an electric circuit by which a
  varying current induces a back emf in that
  circuit or a neighboring circuit.
• Mutual Inductance, M
• Self Inductance, L

http//www.powertransformer.us/primaryvoltage.png
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Mutual Inductance, M

• Effect that occurs in a transformer when a
  varying magnetic field created in the primary
  coil is carried through the iron core to the
  secondary coil, where the varying field induces a
  varying emf.
• M -Es / D Ip/ D t

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M -Es D Ip/ D t

• Shows the ratio of induced emf in one circuit to
  the rate of change of current in the other
  circuit.
• M, inductance, Henry
• Es, average induced emf across secondary
• D Ip/ D t, time rate of change in current in
  primary coil
• - sign, induced v opposes D I (Lenzs law)

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Two coils have a mutual inductance of 1.25
henrys. Find the average emf induced in the
secondary if the current in the primary builds up
to 10.0 amp in 0.0250 sec after the switch is
closed.

• M - Es So, Es -M DIp
• DIp/D t D t
• Es -1.25 h (10.0 a)
• 0.0250 s
• Es -500. v or 5.00 x 102 v

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Self Inductance

• Ratio of induced emf across a coil to the rate of
  change of current in the coil
• L -E / D I / D t
• L, henry
• I, current, amp
• t, time, sec

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Transformer

• Two separate coils of wire placed near one
  another that are used to increase or decrease AC
  voltages with little loss of energy.
• It contains a Primary coil and a Secondary coil
• When the primary is connected to AC voltage, the
  changing current creates a varying magnetic field
  that is carried through the core to the secondary
  coil.

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Transformer, cont.

• In the secondary coil, the varying field induces
  a varying emf. This is called mutual inductance
• Secondary voltage secondary turns
• Primary voltage primary turns
• Power Voltage x Current

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Transformers lose no power

• Pp Ps ? Vp Ip Vs Is
• Transformer Equation
• Is Vp Np
• Ip Vs Ns

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Transformer Problem
A step-up transformer has a primary coil
consisting of 200 turns and a secondary coil that
has 3000 turns. The primary coil is supplied
with an effective AC voltage of 90.0v. A) What is
the Vs? B) If Is 2.00a, find Ip. C) What is
the power in the primary circuit?

• A. Vs NsVp/Np 3000(90.0V) / 200 1.35 kV
• B. Pp Ps, VpIp VsIs ? Ip VsIs/Vp
• Ip 1350v(2.00a) / 90.0v 30.0a
• C. Pp Vp Ip 90.0v(30.0a) 2.70 kW