Chapter 29 Sources of Magnetic Fields

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Chapter 29 Sources of Magnetic Fields

• Danish Physicist
• Hans Christian Oersted (1777-1851) discovers
  a current carrying wire deflects a compass
  (magnet) in 1819
• English Physicist Michael Faraday (1791-1867)
  changing currents can induce a voltage in a
  nearby circuit
• American Physicst Joseph Henry (1797-1878) shows
  that the motion of a magnet produces same effect
  
• Biot and Savart investigate phenomena and
  discover
• B obeys an inverse square law
• B is perpendicular to direction of current and
  displacement from current (wire)
• B is proportional to the sine of the angle
  between current and displacement

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The B-field near a long straight wire with
current i curls around the wire
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Dipole Field
Dipole Magnet or current loop can produce the
same magnetic field B-field curls around the
current loop! Implies a second right hand rule
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Moving charge create B-Fields
Moving charges are the source of magnetic fields
Write moving charge in terms of current
Then,
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Biot - Savart Law
is the magnetic constant mo is the
permeability of free space (vacuum)
We add up (integrate) along the wire to
determine
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Biot-Savart Law applied to important geometries

• Straight Wire (perpendicular bisector)
• Circular coil

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Straight Wire
The magnetic field points into the page
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B for a wire with current i right hand rule
defines direction of the magnetic field
The magnetic field points out of the page at the
point c
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Arc of a circular wire
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Circular coil

• Examining the symmetry shows will contribute
  nothing to the final field, so

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Circular coil
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Second Right Hand Rule
Put thumb in direction of the current and curl
fingers around the wire. Your fingers give the
direction of the B-field lines
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Circular Current Loop
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Force between parallel conductors

• First consider the magnetic field generated by
  wire a current ia in the vicinity of wire b
• Then determine the force this field exerts on
  wire b

What is the magnitude and direction of Fab?
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Circular coil as a magnetic dipole
if xgtgtR
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Example Problem 3

• Two electric transmission lines each carry 100 A
  in opposite directions. If they are separated by
  0.50 m, what is the force/ length between them?
  Is the force one of attraction or repulsion?