Announcements

1
Announcements

• Homework 5 is due at end of class on Friday March
  10
• Posted on WebCT

2
A Brief History of Magnets

• Ancient Greeks and Chinese discovered that
  lodestone (magnetite) exerted a force on iron
  objects and if suspended always pointed in a
  specific direction
• Furthermore, it was seen that iron objects could
  be permanently magnetized through exposure to a
  magnet
• This proved particularly useful for navigation
• In 1820, Oersted discovered an electric current
  would deflect a compass needle, establishing a
  connection between electricity and magnetism
• Force exerted on moving charges no force exerted
  on charges at rest
• Many studies led to a good understanding of
  classical electricity and magnetism in the 19th
  century
• In 1905, Einsteins theory of special relativity
  showed magnetism was really Coulombs law in a
  moving frame
• If you moved along with the charges, you would
  only see electric forces

3
Magnetic Force

• The magnetic force depends on a particles
  charge, velocity, and B, the magnetic field
• We will see how to calculate B later on for
  now, we will just take it as a given
• Magnetic force is perpendicular to directions of
  v and B
• Negative charges have force in opposite direction
  to positive charges
• The magnetic field is like the electric field in
  that it allows us to separate the source (i.e.,
  a magnet) from the force it produces on a
  particular charge

4
Earths Magnetic Field

• Magnets have two poles
• North and South poles
• Opposite poles attract, like poles repel
• Example Earths magnetic field
• South magnetic pole located in northern Canada
• North magnetic pole of compass is attracted to
  south magnetic pole of earth, causing the compass
  needle to point in a northerly direction
• Earths magnetic poles are on the move
• South pole about to defect from Canada
• Trajectory has it arriving in Siberia in 50 years

5
Visualizing the Magnetic Field

• Can use iron filings to visualize a magnetic
  field
• Filings line up along direction of magnetic field
• Each filing becomes a little magnet with a north
  and south pole
• North pole of one filing attracted to south pole
  of next filing
• Example Horseshoe magnet
• Example Bar magnet
• Earths magnetic field is like the bar magnet
• Magnetic field vertically downward at south
  magnetic pole, upward at northern magnetic pole
• At other locations, have non-vertical component
  of magnetic field pointing toward the magnetic
  pole
• What happens if I break a magnet in two?
• Get two new magnets, each with a north and south
  pole

6
Motion of Charged Particle in Uniform B

• Suppose we have a constant magnetic field pointed
  up
• Examine the motion of a charged particle moving
  horizontally
• Acceleration is always perpendicular to velocity,
  so we have circular motion
• Equation with momentum is valid for relativistic
  particles

7
Example Fermilab

• Superconducting magnets produce a magnetic field
  of 4T
• Tesla is the SI unit for magnetic field
• Earths magnetic field is 0.0005T
• R 1 km for high energy protons, anti-protons at
  Fermilab

8
Magnetic Force on Current

• We have defined the magnetic field in terms of
  its force on a charged particle
• What about when we have a wire carrying a current
• Many moving charges, each has a force exerted on
  them
• Consider the force on a charge dq that passes
  through a section of wire of length dL
• To get force on wire, integrate over length of
  wire