Magnetic Fields

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Chapter 29

• Magnetic Fields

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Outline

• Magnetic fields (29.1)
• Magnetic force on a charged particle moving in a
  magnetic field (29.1)
• Magnitude
• Direction right-hand rule
• Magnetic force on a current-carrying conductor
  (29.2)
• Straight wire
• Curved wire
• Wire loop

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Magnetic fields
A spoon-shaped compass
Lifting fingerprints by a magnetic brush
Magnetic field lines
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Magnetic force on a charged particle moving in a
magnetic field

• Vector expression for the magnetic force on a
  charged particle moving in a magnetic field FB
  qv ? B
• Magnitude of the magnetic force FB
  qvB sin ?
• If ? 0? or 180?, v // B, FB 0.
• If ? 90?, v ? B, FB is maximum.
• If v 0, non-moving charge, FB 0.
• Direction of the magnetic force? use the
  right-hand rule.
• SI unit of B the tesla (T) 1 T 1 N/(Cm/s)
• Another unit in common use gauss (G) 1 T 104
  G.

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Right-hand rule

• FB is ? to both v and B FB is ? to the plane
  formed by v and B.
• To find the direction of FB qv ? B
• (1) Find the direction of the cross product v ?
  B, using the right-hand rule.
• Right-hand rule Point the four fingers of your
  right hand along the direction of v and curl them
  toward B. The extended thumb points in the
  direction of v ? B.
• (2) If q is , FB is in the direction of your
  thumb if q is -, FB is opposite the direction
  of your thumb.

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Quick Quiz

• An electron moves in the plane of this paper
  toward the top of the page. A magnetic field is
  also in the plane of the page and directed toward
  the right. The direction of the magnetic force on
  the electron is
• (a) toward the top of the page, (b) toward the
  bottom of the page, (c) toward the left edge of
  the page, (d) toward the right edge of the page,
  (e) upward out of the page, (f) downward into the
  page.

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Example 29.1 An electron moving in a magnetic
field

• An electron in a television picture tube moves
  toward the front of the tube with a speed of 8.0
  x 106 m/s along the x axis. Surrounding the neck
  of the tube are coils of wire that create a
  magnetic field of magnitude 0.025 T, directed at
  an angle of 60? to the x axis and lying in the xy
  plane. Calculate the magnetic force on the
  electron. Find both the magnitude and direction
  of the force.
• (A) Use equation FB qv ? B.
• (B) Use a vector expression.

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Important differences between eclectic and
magnetic forces

• The electric force acts along the direction of
  the electric field, whereas the magnetic force
  acts perpendicular to the magnetic field.
• The electric force acts on a charged particle
  regardless of whether the particle is moving,
  whereas the magnetic force acts on a charged
  particle only when the particle is in motion.
• The electric force does work in displacing a
  charged particle, whereas the magnetic force
  associated with a steady magnetic field does no
  work when a particle is displaced because the
  force is perpendicular to the displacement.

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Magnetic force acting on a current-carrying
conductor

• Magnetic force on a straight segment of
  current-carrying wire in a uniform magnetic
  field FB I L ? B.
• L a vector direction along I magnitude equals
  to L.
• Magnetic force on a curved current-carrying wire
  in a uniform magnetic field
• Net magnetic force acting on any closed current
  loop in a uniform magnetic field

Straight wire
Curved wire
Closed current loop
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An example
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Quick Quiz

• Rank the wires according to the magnitude of the
  magnetic force exerted on them.

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Example 29.2 Force on a semicircular conductor

• A wire bent into a semicircle of radius R forms a
  closed circuit and carries a current I. The wire
  lies in the xy plane, and a uniform magnetic
  field is directed along the positive y axis. Find
  the magnetic force acting on the straight portion
  of the wire and on the curved portion.