Download 27 Motion of Charged Particles in a Magnetic Field

 Physics
 Comb. Sci.
NSS Physics in Life In-class Worksheets
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27 Motion of Charged Particles in a Magnetic Field
27.1 Electric current and electron drift velocity
Learning objectives

Derive the relation I = nAvQ between electron drift velocity and electric current.
Key ideas

In the absence of electric field, the free electrons in an isolated metal wire move
randomly and collide with the _______________________ in the wire.

In the presence of electric field, the electrons experience electric forces and drift
slowly in the _______________ direction of the electric field at the
_______________ velocity.

The current carried by a conductor can be expressed as

The _______________ velocity (~10−5 m s−1) of free electrons is extremely small
compared with their mean speed (~106 m s−1).

_______________________ is set up along the circuit as soon as the circuit is
closed and all free electrons start to circulate around. Electrical energy is then
converted into other forms of energy in the loads, regardless of the magnitude of
the drift velocity.
Follow-up
Checkpoint ( p.319)
Exercise ( p.320)
ISBN: 9789880059414
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Example 27.1A
 Physics
 Comb. Sci.
Electric current ( p.319)
Iron has 1.7  1029 electrons per cubic metre. Estimate the size of current produced if
electrons in an iron wire of diameter 1 mm drift at about 104 m s1. The magnitude of
the charge of an electron is 1.60 × 10−19 C.
Solution
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2.
ISBN: 9789880059414
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 Physics
 Comb. Sci.
NSS Physics in Life In-class Worksheets
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27.2 Magnetic force on a moving charge
Learning objectives

Represent the magnetic force on a moving charge by F = BQv sin .
Key ideas

The magnitude of the magnetic force on a moving charged particle in a magnetic
field is given by

The direction of the magnetic force on the charged particle can be determined by
____________________________________.

To pass through the crossed fields in a velocity selector without deflection, the
speed of the particles must be

The motion of a charged particle in a uniform magnetic field depends on the angle
between its initial velocity and the direction of the field, which can be
summarized as

values of 
type of motion
= 0° or 180°
______________________________
= 90°
______________________________
0° << 90° or 90° << 180°
______________________________
In a mass spectrometer, the radii of the semi-circular paths taken by the charged
particles depend on their ______________________________ ratios, so that
different particles can be separated and identified.
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 Physics
 Comb. Sci.
Follow-up
Checkpoint ( p.326)
Checkpoint ( p.330)
Exercise ( p.330)
4.
ISBN: 9789880059414
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 Physics
 Comb. Sci.
Example 27.2A
NSS Physics in Life In-class Worksheets
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Magnetic force acting on a helium nucleus
( p.323)
A helium nucleus of charge +2e enters a uniform magnetic field at 1.5  107 m s−1. The
magnetic field has a magnitude of 0.8 T and points into the paper. The magnitude of
the charge of an electron is 1.60 × 10−19 C.
+2e
1.5  107 m s−1
(a) Find the magnitude and direction of the force acting on the nucleus initially.
(b) Sketch the path of the helium nucleus.
Solution
(a) _________________________________________________________________
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
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(b)
ISBN: 9789880059414
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Example 27.3A
 Physics
 Comb. Sci.
Velocity selector ( p.323)
In the following velocity selector, the metal plates are 2 cm apart. The electric field
between the metal plates is controlled by the voltage across the plates. A pair of slab
magnets is used to provide a uniform magnetic field of magnitude 0.8 T. When the
voltage is adjusted to 40 V, an ion projected at right angle to the magnetic field passes
through the gap without deflection. Find the velocity v of the ion.
uniform
magnetic field
v
2 cm
Solution
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6.
ISBN: 9789880059414
©Pearson Education Asia Limited 2010
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 Physics
 Comb. Sci.
Example 27.4A
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Mass spectrometer ( p.328)
In a mass spectrometer, charged particles with the same velocity, 1.52  107 m s1, are
projected at right angles into a uniform magnetic field of magnitude 1.5 T.
(a) A particle of charge 3.2  1019 C moves in a path of radius 0.21 m in the
magnetic field. What is the mass of the particle?
(b) If another charged particle moves in the magnetic field with the same deflection,
what conclusion can be drawn?
Solution
(a) _________________________________________________________________
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(b)
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ISBN: 9789880059414
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27.3
 Physics
 Comb. Sci.
Hall effect
Learning objectives

Know about Hall effect and derive the equation VH 

Examine magnetic fields using a Hall probe.
BI
for Hall voltage.
nQb
Key ideas

When a current passes through a conductor placed in a uniform magnetic field,
each of the charge carriers experiences a ______________________ and deflects
to the surfaces. The deflection of the moving charged carriers leads to an excess
or a deficiency of ______________________ on the upper or lower surface of the
conductor.

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
_______________ the magnetic force on it. These two forces ________________
each other in the steady state.
8.
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 Physics
 Comb. Sci.

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The ___________________ 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

A ___________________ is a device based on the Hall effect to measure a
magnetic field.
Follow-up
Checkpoint ( p.338)
Checkpoint ( p.340)
Exercise ( p.340)
ISBN: 9789880059414
©Pearson Education Asia Limited 2010
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Example 27.5A
 Physics
 Comb. Sci.
Hall probe ( p.336)
The following shows a thin copper film inside a Hall probe. When a current of 2 A
flows through the film, the Hall voltage developed across the width of the film is
1.97 μV. The thickness and width of the copper film are 0.3 mm and 3 mm respectively.
The electron density of copper is 8.47  1028 m−3.
0.3 mm
2A
1.97μV
3 mm
B
(a) What is the magnitude of the magnetic field B?
(b) Estimate the average drift velocity of the electrons in the copper film.
Solution
(a) _________________________________________________________________
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(b) _________________________________________________________________
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10.
ISBN: 9789880059414
©Pearson Education Asia Limited 2010
All rights reserved.