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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

Chapter 19
  • Magnetism

  • Magnetic Fields II
  • Sections 610

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

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
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
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
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

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

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
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

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

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

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
  • Sum all the products of B ?l around the closed

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

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
  • 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

Magnetic Field of a Current Loop Total Field
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

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

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

Magnetic Field in a Solenoid from Ampères Law
  • A cross-sectional view of a tightly wound
  • 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

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

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
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

Magnetic Effects of Electrons Orbits
  • An individual atom should act like a magnet
    because of the motion of the electrons about the
  • 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

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

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
  • That is why most materials are not naturally

Magnetic Effects of Electrons Domains
  • In some materials, the spins do not naturally
  • 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

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

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
  • 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