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
• Sum all products B ?l around the closed path
• 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
  materials to quickly return to an unmagnetized
  state

• When a ferromagnetic core is placed inside a
  current-carrying loop, the magnetic field is
  enhanced since the domains in the core material
  align, increasing the magnetic field