Transcript Motion of Charged Particles in a Magnetic Field

Electricity and Magnetism
Chapter 27
Motion of Charged
Particles in a Magnetic
Field
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Motion of Charged Particles in a Magnetic Field
Electricity and Magnetism
• 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 (~10–5 m s–1) of free electrons is extremely
small compared with their mean speed (~106 m s–1).
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Motion of Charged Particles in a Magnetic Field
Electricity and Magnetism
• 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.
Example 27.1
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Microscopic view
of electric current
Checkpoint (p.319) O
Motion of Charged Particles in a Magnetic Field
Electricity and Magnetism
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
≠ 90˚
Q →q +ve
–ve
q = 90˚
The direction of the force
can be determined by
Fleming’s left hand rule.
Example 27.2
Experiment 27.1
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Motion of Charged Particles in a Magnetic Field
Electricity and Magnetism
• To pass through the crossed fields in a velocity selector
without deflection, the speed of the particles must be
E
v
B
Velocity selector
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Example 27.3
Checkpoint (p.326) O
Motion of Charged Particles in a Magnetic Field
Electricity and Magnetism
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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Motion of Charged Particles in a Magnetic Field
Electricity and Magnetism
• 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:
mv 2
 BQv
r
mv
r
QB
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Motion of Charged Particles in a Magnetic Field
Electricity and Magnetism
• 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
mv
r
QB
The radius r differs if the charge to
mass ratios (Q / m) differs.
Mass spectrometer
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Example 27.4
Motion of Charged Particles in a Magnetic Field
Checkpoint (p.330) O
Electricity and Magnetism
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
A conductor
conductor with
with negative
positive charge
charge carriers
carriers
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Motion of Charged Particles in a Magnetic Field
Electricity and Magnetism
• 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
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A conductor with
negative charge carriers
Motion of Charged Particles in a Magnetic Field
Electricity and Magnetism
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
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A conductor with
negative charge carriers
Motion of Charged Particles in a Magnetic Field
Electricity and Magnetism
• 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
BI
VH 
nQb
VH
Checkpoint (p.338) O
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Example 27.5
Motion of Charged Particles in a Magnetic Field