AP Unit III D1' Magnetic Fields

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AP Unit III D1. Magnetic Fields

• Students should understand the force experienced
  by a charged particle in a magnetic field, so
  they can
• (a) Calculate the magnitude and direction of the
  force in terms of q, v, and B, and explain why
  the magnetic force can do no work.
• (b) Deduce the direction of a magnetic field from
  information about the force experienced by
  charged particles moving through that field.
• (c) Describe the paths of charged particles
  moving in uniform magnetic fields.

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• (d) Derive and apply the formula for the radius
  of the circular path of a charge that moves
  perpendicular to a uniform magnetic field.
• (e) Describe under what conditions particles will
  move with constant velocity through crossed
  electric and magnetic fields.

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Magnetic Fields

• Magnetic Field Strength B magnetic flux ?/ area
  A
• B ?/A.
• B is measured in Teslas (T), magnetic flux ? is
  measured in Webers (Wb), and Area is measured in
  m2

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• The magnetic field around a bar magnet is spider
  shape
• The direction of the field lines is from North to
  South (the direction the north pole of a magnet
  would go in if placed in the field.)
• The magnetic field around a current carrying wire
  B ?0 I /2 ?a where ?0 is the magnetic
  permeability of free space or vacuum permeability
  4? x 10-7 (T m) / A

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Magnetic Field in a loop of current carrying wire.

• I

-
Current I

-

Magnetic field around single current carrying wire
Magnetic field around loop of current carrying
wire
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• x x
• x x x
• x x x x x
• x x x
• x x

x means magnetic field arrows going INTO paper
towards direction of North
If current goes counterclockwise then this side
is north pole of electromagnet
If current goes clockwise then this side is south
pole of electromagnet
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Magnetic Force _ The Motor Effect

• The magnetic force on a wire is given by FBILsin
  ?
• The magnetic force on a charge is given by F
  Bqv
• The direction of the force is given by the right
  hand rule for conventional current (positive
  charges)
• X means magnetic field going into the page
• ? means magnetic field coming out of the page.

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Direction of force on a positive charge (Fig 19-7
p629)
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• A charge entering a magnetic field will describe
  a circle.
• Magnetic force centripetal force
• Bqv mv2/r
• Calculate v for an electron describing 12 cm
  radius circle in magnetic field 4 x 10-4 T.

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• Bev mv2/r
• v rBe/m
• v 12 x 10-2 x 4 x 10-4 x 1.6 x 10-19/ 3.31 x
  10-34
• v

If the particle moves under constant velocity
under crossed electric and magnetic fields the
electrical and magnetic forces are equal and
opposite. Eq Bqv
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• This effect is used in particle accelerators to
  determine the mass of an unknown particle.
• The charged particle is accelerated into a known
  magnetic field. The radius of path it describes
  tells us the mass since Bqv mv2/r them m
  Bqr/v.
• x x x x x
• x x x x x

If the particle is not charged it can be
accelerated into a particle which is.
v
B
q
r
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Crossed magnetic and electric fields

• x x x x x x x x
• x x x x x x x x

V 2000V

d 0.5 cm
B .007 T
-
What is magnitude of charge on particle and which
direction will it move in ? Homework Questions
AP U III D 1Q1-10p652 all.