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## Magnetism

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### Magnetic Fields II. Sections 6 10. Motion of a Charged Particle in a Uniform Magnetic Field ... Magnetic Fields. Long Straight Wire. A current-carrying wire ... – PowerPoint PPT presentation

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Title: Magnetism

1
Chapter 19
• Magnetism

2
• Magnetic Fields II
• Sections 610

3
Motion of a Charged Particle in a Uniform
Magnetic Field
• Consider a particle moving in an external
magnetic field so that its velocity is
perpendicular to the field
• The force is always directed toward the center of
the circular path
• The magnetic force causes a centripetal
acceleration, changing the direction of the
velocity of the particle

4
Motion of a Charged Particle in a Uniform
Magnetic Field, cont
• Equating the magnetic and centripetal forces
• Solving for the radius r
• r is proportional to the momentum mv of the
particle and inversely proportional to the
magnetic field
• Sometimes called the cyclotron equation

Active Figure Motion of a Charged Particle in a
Uniform Magnetic Field
5
The Mass Spectrometer Separating Isotopes
• The cyclotron equation can be applied to
the process of separating isotopes
• Singly ionized isotopes are injected into a
velocity selector
• Only those isotopes with velocity v E/B pass
into the deflection chamberWhy?
• Isotopes travel in different circular paths
governed by the cyclotron equationtherefore
different mass isotopes separate

Active Figure The Mass Spectrometer
6
Particle Moving in an External Magnetic Field
• If the particles velocity is not perpendicular
to the magnetic field, the path followed by the
particle is a spiral
• The spiral path is called a helix

Active Figure A Charged Particle with a Helical
Path
7
Charged Particles Trapped in the Earths
Magnetic FieldAuroras
• Charged particles from the Sun enter the Earths
magnetic field
• These particles move in spirals around the lines
of magnetic field
• This causes them to become trapped in the Earths
magnetic field
• An aurora is caused by these trapped charged
particles colliding with atoms in the upper
atmosphereproducing beautiful displays of light

8
Hans Christian Oersted
• 1777 1851
• Best known for observing that a compass needle
deflects when placed near a wire carrying a
current
• First evidence of a connection between electric
and magnetic phenomena

9
Magnetic Fields Long Straight Wire
• A current-carrying wire produces a magnetic field
• The compass needle deflects in directions tangent
to the circle
• The compass needle points in the direction of the
magnetic field produced by the current

Active Figure Magnetic Field Due to a Long
Straight Wire
10
Direction of the Field of a Long Straight Wire
• Right Hand Rule 2
• Grasp the wire in your right hand
• Point your thumb in the direction of the current
• Your fingers will curl in the direction of the
field

11
Magnitude of the Field of a Long Straight Wire
• The magnitude of the field at a distance r from a
wire carrying a current of I is
• µo 4 ? x 10-7 T.m / A
• µo is called the permeability of free space

12
André-Marie Ampère
• 1775 1836
• Credited with the discovery of electromagnetism
• Relationship between electric currents and
magnetic fields
• Mathematical genius evident by age 12

13
Ampères Law
• André-Marie Ampère found a procedure for deriving
the relationship between the current in a wire
and the magnetic field produced by the wire
• Ampères Circuital Law
• ?B ?l µo I
• Sum over the closed path around the current I
• Choose an arbitrary closed path around the
current
• Sum all the products of B ?l around the closed
path

14
Ampères Law to Find B for a Long Straight Wire
• Sum over a closed circular path around current I
• ?B ?l µo I
• B2?r µo I
• The magnitude of the magnetic field a distance r
from the wire

15
Magnetic Field of a Current Loop
• The strength of a magnetic field produced by a
wire can be enhanced by forming the wire into a
loop
• All the segments, ?x, contribute to the field,
increasing its strength
• The magnitude of the magnetic field at the center
of a circular loop with a radius R

16
Magnetic Field of a Current Loop Total Field
17
Magnetic Field of a Solenoid
• If a long straight wire is bent into a coil of
several closely spaced loops, the resulting
device is called a solenoid
• It is also known as an electromagnet since it
acts like a magnet only when it carries a current

18
Magnetic Field of a Solenoid, 2
• The field lines inside the solenoid are nearly
parallel, uniformly spaced, and close together
• This indicates that the field inside the solenoid
is nearly uniform and strong
• The exterior field is nonuniform, much weaker,
and in the opposite direction to the field inside
the solenoid

19
Magnetic Field in a Solenoid, 3
• The field lines of the solenoid resemble those of
a bar magnet dipole magnetic field

20
Magnetic Field in a Solenoid from Ampères Law
• A cross-sectional view of a tightly wound
solenoid
• If the solenoid is long compared to its radius,
we assume the field inside is uniform and outside
is zero
• Apply Ampères Law to the blue dashed rectangle
• The magnitude of the field inside a solenoid is
constant at all points far from its ends
• n is the number of turns per unit length
• n N / l

21
Magnetic Force Between Two Parallel Conductors
• The force on wire 1 is due to the current in wire
1 and the magnetic field produced by wire 2
• The force per unit length is

22
Force Between Two Conductors, cont
• Parallel conductors carrying currents in the same
direction attract each other
• Parallel conductors carrying currents in the
opposite directions repel each other

Active Figure Force Between Long Parallel Wires
23
Defining Ampere and Coulomb
• The force between parallel conductors can be used
to define the Ampere (A)
• If two long, parallel wires 1 m apart carry the
same current, and the magnitude of the magnetic
force per unit length is 2 x 10-7 N/m, then the
current is defined to be 1 A
• The SI unit of charge, the Coulomb (C), can be
defined in terms of the Ampere
• If a conductor carries a steady current of 1 A,
then the quantity of charge that flows through
any cross section in 1 second is 1 C

24
Magnetic Effects of Electrons Orbits
• An individual atom should act like a magnet
because of the motion of the electrons about the
nucleus
• Each electron circles the atom once in about
every 10-16 seconds
• This would produce a current of 1.6 mA and a
magnetic field of about 20 T at the center of the
circular path
• However, the magnetic field produced by one
electron in an atom is often canceled by an
oppositely revolving electron in the same atom
• The net result is that the magnetic effect
produced by electrons orbiting the nucleus is
either zero or very small for most materials

25
Magnetic Effects of Electrons Spins
• Electrons also have spin
• The classical model is to consider the electrons
to spin like tops
• It is actually a quantum effect

26
Magnetic Effects of Electrons Spins, cont
• The field due to the spinning is generally
stronger than the field due to the orbital motion
• Electrons usually pair up with their spins
opposite each other, so their fields cancel each
other
• That is why most materials are not naturally
magnetic

27
Magnetic Effects of Electrons Domains
• In some materials, the spins do not naturally
cancel
• Such materials are called ferromagnetic
• Large groups of atoms in which the spins are
aligned are called domains
• When an external field is applied, the domains
that are aligned with the field tend to grow at
the expense of the others
• This causes the material to become magnetized

28
Domains, cont
• Random alignment (left) shows an unmagnetized
material
• When an external field is applied, the domains
aligned with B grow (right)

29
Domains and Permanent Magnets
• In hard magnetic materials, the domains remain
aligned after the external field is removed
• The result is a permanent magnet
• In soft magnetic materials, once the external
field is removed, thermal agitation causes the