Chapter 27 Motion of Charged Particles in a Magnetic Field

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Chapter 27 Motion of Charged Particles in a
Magnetic Field
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• In the presence of electric field, the electrons
  experience electric forces and drift slowly in
  the opposite direction of the electric field at
  the drift velocity.
• The drift velocity (105 m s1) of free
  electrons is extremely small compared with their
  mean speed (106 m s1).

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• The current I carried by a conductor can be
  expressed as

I nAvQ

• where n is the number of free charge carriers
  per unit volume
• A is the cross-sectional area of the conductor
• v is the drift velocity of the charge carriers
• Q is the charge carried by the charge carriers.

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27.2 Magnetic force on a moving charge

• The magnetic force F on a moving charged particle
  with a velocity v in a magnetic field B at an
  angle q is given by

F BQv sin q
The direction of the force can be determined by
Flemings left hand rule.
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• To pass through the crossed fields in a velocity
  selector without deflection, the speed of the
  particles must be

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Motions of charged particles in uniform magnetic
field

• The motion of a charged particle in a uniform
  magnetic field B depends on the angle q between
  its initial velocity v and the direction of the
  field.

q 0 or 180
F 0
rectilinear motion
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• The motion of a charged particle in a uniform
  magnetic field B depends on the angle q between
  its initial velocity v and the direction of the
  field.

q 90
circular motion
The centripetal force is provided by the magnetic
force acting on the particle
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• In a mass spectrometer, the radii of the
  semi-circular paths taken by the charged
  particles depend on their charge to mass ratios,
  so that different particles can be separated and
  identified.

Recall that the radius r of the circular path is
given by
The radius r differs if the charge to mass ratios
(Q / m) differs.
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27.3 Hall effect
Deflection of charge carriers in conductor

• When a current passes through a conductor placed
  in a uniform magnetic field, each of the charge
  carriers experiences a magnetic force and
  deflects to the surfaces.

A conductor with positive charge carriers
A conductor with negative charge carriers
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• The deflection of the moving charged carriers
  leads to
• an excess of positive (or negative) charge
  carriers on the upper surface, and
• a deficiency of positive (or negative) charge
  carriers on the lower surface.

A conductor with positive charge carriers
A conductor with negative charge carriers
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Hall voltage

• A p.d. is developed across the conductor due to
  the deflected charge carriers.
• Each charge carrier moving in the conductor
  experiences an electric force that opposes the
  magnetic force on it.
• These two forces balance each other in the steady
  state.

A conductor with positive charge carriers
A conductor with negative charge carriers
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• The Hall effect is the production of a Hall
  voltage across the opposite surfaces of a
  current-carrying conductor placed in a magnetic
  field, which is given by