Sources of Magnetic Fields

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Chapter 30

• Sources of Magnetic Fields

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Hans Christian Oersted

• College professor in Copenhagen
• 1820Discovered that current running through a
  wire would deflect a compass
• By accident, while doing demos
• Had no idea how or why it happened
• Published in Latin, so at least he sounded smart

1777-1851
43 years old in 1820
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Andre-Marie Ampere

• Father was guillotined during the French
  revolution, and his wife died young in 1803
• Picked up on Oersteds work
• Defined the connection between current and
  magnetism by examining forces between parallel
  wires

1775-1836
45 years old in 1820
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Michael Faraday

• Started life as a book binder
• Discovers that moving magnets will produce an
  induced current in wires that arent even
  connected to a power source
• First to describe electric and magnetic forces
  using fields
• Remember, the idea that invisible lines are
  running everywhere, and that we can count them,
  is not exactly self-evident

1791-1867
29 years old in 1820
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James Clerk Maxwell

• Summarizes everyones findings mathematically
• Demonstrates the connection between electric
  fields and magnetic fields
• Discovers and defines electromagnetic waves
• Sorta mathematically discovered the precise speed
  of light

1831-1879
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Biot-Savart Law

• Way of calculating the magnetic field due to a
  segment of current carrying wire
• dB section of magnetic field caused by the
  current
• I current
• dl section of length of wire
• r distance between dl and the point in space

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Magnetic field of a wire

• Field lines circle around the wire
• Direction from a right hand rule
• Thumb current
• Fingers wrap around in the direction of the
  circular field lines
• Equation of straight wires
• r distance from wire
• ?0 4? x 10-7 Tm/A
• Permeability of free space

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Magnetic field of a loop

• In circular loops, the magnetic fields line up
  and add up in the middle
• Equation for center of loop
• R radius of the loop
• N number of loops

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Magnetic field of solenoids

• When you loop enough times that the length of the
  coil is significantly greater than the radius of
  each loop, its called a solenoid
• The magnetic field inside is greatly enhanced and
  truly matches a bar magnet
• Equation
• N number of loops
• L length

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Force between parallel wires

• Each wire is affected by the others B-field
• Equation for B-field of wire 1 is given
• The force on wire 2 is F ILB
• Attract if currents run in same direction
• Repel if currents run in opposite directions

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Definition of Ampere

• Ampere is defined by the magnetic forces between
  wires
• When two currents are identical in the wires, and
  F/L 2 x 10-7N/m, each current is defined as 1A.
• Coulomb is defined by the Ampere
• 1C of charge flows through a wire with 1A of
  current in 1s

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Amperes Law

• Useful for systems with good magnetic symmetry
• Similar to Gausss law for electric fields
• Funny shaped fields just make the math messier
• Integral represents area inside a closed loop
• B magnetic field
• ds portion of length around a the loop
• I total current running through the enclosed
  area

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Inside a wire
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A torroid
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Force on a current segment
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Solenoids, reloaded
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Magnetic Flux

• Flux (?B)the number of field lines passing
  through a given area
• Units of Webers (Wb)
• 1 Wb 1 Tm2
• ? angle between plane of the loop and the
  B-lines

For constant B-fields
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Magnetic Flux
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Gausss Law, magnetic style

• Net magnetic flux through any closed surface is
  zero
• All field lines going in must go out
• Electrical flux does not have to equal zero
  because positive charges can exist separate from
  negative ones
• Magnetic poles cannot be isolated from one another