Magnetism

Summary

• A magnet is an object that exhibits magnetic properties such as…
  • exerting an attractive force on iron or other ferromagnetic materials
  • exerting both attractive and repulsive forces on other magnets
  • deflecting the path of a moving charged particle
• Magnetic poles
  • Regions on a magnet where the forces are the strongest.
  • Come in two types — north pole and south pole
    • often shortened to north and south
    • or abbreviated N and S
  • Magnetic poles always occur in north-south pairs called dipoles.
    • Combinations of of dipoles are called multipoles.
    • Some multipole arrangements have special names
      • two dipoles form a quadrupole
      • three dipoles form a hexapole or sextupole
      • four dipoles form an octupole
  • Magnetic monopoles do not seem to exist.
    • When a dipole magnet is broken, all of its pieces are also dipoles.
    • This is true down to the subatomic level. Electrons, protons, and neutrons are dipoles.
    • Some theoretical physicists have predicted the existence of particles with a single magnetic pole, but these claims have not been verified experimentally.
• Rule of action
  • Like poles repel.
  • Opposite poles attract.
• Compass
  • A compass is any dipole magnet that is free to rotate.
• Magnetic field
  • The direction of the magnetic field is determined by following the north pole of a compass.
    • Magnetic field lines…
      • diverge from the north pole of a magnet
      • converge on the south pole of a magnet
  • The strength of the magnetic field at any location is proportional to the density of the lines drawn.
  • Magnetic field lines never intersect.
    • The field can only point in one direction at any location.
  • Magnetic field lines form closed loops.
    • Magnetic field lines reconnect inside a magnet.
    • This explains why when a magnet is broken, all of its pieces are also dipoles.
  • The symbol for magnetic field is an uppercase, bold B (vector notation) or an uppercase, italic B (for the magnitude only).
    • The reason for this choice of symbol is unknown.
    • The magnetic field is also known as the B field, magnetic flux density, and magnetic induction.
  • The SI unit of magnetic field is the tesla [T].
    • In terms of other units, the tesla is also
      • a newton per ampere meter (from the Lorentz force law)
      • a weber per meter square (from Faraday's law)
      • a kilogram per ampere second squared (in SI base units)

      ⎡ ⎢ ⎣	T =	N	=	Wb	=	kg	⎤ ⎥ ⎦
      		Am		m2		As2

    • 1 T is a very strong magnetic field.
• Geomagnetism
  • The earth is basically a giant dipole magnet.
  • A compass will rotate until it aligns with the Earth's magnetic field.
    • The north pole of a compass tends to point north (toward the Earth's north magnetic pole).
    • The south pole of a compass tends to point south (toward the Earth's south magnetic pole).
  • The magnetic poles of the Earth (locations on the surface of the Earth where the magnetic field is the strongest) are near the geographic poles (locations where the spin axis of the Earth intersects its surface).
    • The north magnetic pole of the Earth is currently in the Arctic Ocean near the north geographic pole. A compass would point straight down at this location making it a south pole.
    • The south magnetic pole of the Earth is currently in the Indian Ocean near Antarctica. A compass would point straight up at this location making it a north pole.
  • The magnetic axis of the Earth differs from its rotational axis by about 10°.
  • The magnetic field strength on the surface of the Earth is around 45±15 μT.
• Materials
  • Ferromagnetic materials…
    • are strongly attracted to a magnet
    • have atoms that strongly align to an external magnetic field
    • are capable of forming permanent magnets
    • include the elements…
      • iron, cobalt, nickel (transition metals)
      • dysprosium, gadolinium (rare earths)
    • include some minerals and alloys
      • Some iron minerals are magnetic (e.g. magnetite, Fe₃O₄), some are not (e.g. pyrite, FeS₂)
      • Some steels are magnetic (e.g. ferritic steels), some are not (e.g. austenitic steels)
      • Some alloys of non-ferromagnetic metals are ferromagnetic (e.g. Heusler alloy, Cu₂MnSn)
  • Paramagnetic materials…
    • are weakly attracted to a magnet
    • have atoms that weakly align to an external magnetic field
    • are only ever weak, temporary magnets
    • include most elements, molecules, and compounds (e.g. molecular oxygen, O₂)
  • Diamagnetic materials…
    • are weakly repelled by a magnet
    • have atoms that weakly align opposite to an external magnetic field
    • are only ever weak, temporary magnets
    • include a few elements, molecules, and compounds (e.g. carbon, mercury, water)
  • Superdiamagnetic materials…
    • are strongly repelled by a magnet
      • This property can be used for magnetic levitation (a.k.a. the Meissner effect)
    • do not allow magnetic fields to penetrate below a thin surface layer
    • are are only superdiamagnetic when they are in a superconducting state (below some very low temperature, typically T ≲ 10 K but sometimes as high as T ≲ 100 K)
    • are dealt with in another section of this book
• Types of magnets
  • Permanent magnets are specially processed ferromagnetic materials that will retain their magnetic state indefinitely.
  • Temporary magnets come in two very different types.
    • Induced magnets are ferromagnetic materials that retain their magnetic state only while in the presence of an external magnetic field.
      • The outside surface of a steel refrigerator door is not a magnet, but parts of it will behave like a magnet when a permanent magnet is placed in contact with it.
    • Electromagnets are typically current-carrying coils of wire.
      • Electromagnets only behave like magnets when they are connected to a power source and turned on.