#### The Hall effect

 In 1879 Hall discovered a small electric field EH in a conductor carrying a current I in a magnetic field B.  The electric field EH is perpendicular to both the direction of the magnetic field and the direction of current flow.  Hall used this observation to prove that the current in metal conductors is carried by negative charges.The current in the metal strip shown above is flowing because a power supply establishes an electric field E in the strip.  The conduction electrons move with an average drift velocity vd opposite to the direction of E.  In the uniform field B the magnetic force on each electron is F = -ev × B.  It causes the electrons to drift towards side 1 of the strip, leaving excess positive charge on side 2.  These separated charges produce the electric field EH.  The electrons will stop drifting sideways, when the electric force -eEH cancels the magnetic force -ev × B.  The resulting potential difference across the strip is ΔV = V2 - V2 = EHL = vdBL.  This is known as the Hall potential.  If positive charges were moving in the strip, they would drift towards side 1 and the sign of the Hall potential would change

The Hall effect can be used to measure the strength of the magnetic field perpendicular to a current-carrying metal strip, called a Hall probe.  The dimensions of the probe and the drift velocity for a given power-supply voltage are known.  The potential difference ΔV then yields the magnetic field strength B.

Ferromagnets

Ferromagnetic materials are materials that have magnetic properties similar to those of iron.  They can become permanently magnetized.  Examples of ferromagnetic materials are nickel, cobalt, and alnico, an aluminum-nickel-cobalt alloy.

Magnetic fields are produced by currents.  Permanent magnets are the result of magnetization currents flowing inside the material.  The magnetization currents in materials are a consequence of the electron's spin.  Electrons have an intrinsic property, called spin.  Because they have spin, they have a magnetic moment, similar to a small current loop.  Electrons by themselves act like tiny magnets.  If you pick an axis, an electron's magnetic moment can either be parallel or anti-parallel to this axis.  In an atom the electrons are arranged in orbitals.  An orbiting electron can have an additional magnetic moment similar to the magnetic moment of a tiny current loop.  If all the magnetic moments of the electrons in an atom do not completely cancel out, then the atom will act like a tiny magnet.

When any material is placed into a magnetic field its atoms acquire an induced magnetic moment pointing in a direction opposite to that of the external field.  The material becomes magnetic.  This is called diamagnetism.  The diamagnetic field produced by the material opposes the external field, but, except in superconductors, this diamagnetic field is very weak.  If the atoms of a material have no magnetic moment of their own then diamagnetism is the only magnetic property of the material and the material is called diamagnetic.  Copper is such a material.

Link:  Graphite is a diamagnetic material.  It is repelled by both poles of a magnet.

In paramagnetic materials all the magnetic moments of the electrons in an atom do not completely cancel out, and each atom has a magnetic moment.  However, in paramagnetic materials such as aluminum, neighboring atoms do not align themselves with each other in the absence of an external magnetic field.  The magnetic fields produced by the individual atoms therefore cancel each other.  An external magnetic field tends to align the magnetic moments in the direction of the applied field, but thermal motion tends to randomize the directions.  The paramagnetic field produced by the aligned magnetic moments reinforces the external field, but at room temperatures it is on the average only approximately 10 times stronger than the diamagnetic field and therefore still very weak.

Link:  Liquid oxygen is a paramagnetic material.  It is attracted to the poles of a magnet.

In ferromagnetic materials, the spins of neighboring atoms do align even in the absence of an external field (through a quantum effect known as exchange coupling), resulting in small (a tenth of a millimeter, or less) neighborhoods called domains where all the spins are aligned.  When a piece of ferromagnetic material is placed into an external magnetic field, two things happen.

 The spins in each domain shift so that the magnetic moments of the electrons become more aligned with the direction of the field. Domains aligned with the field expand and take over regions previously occupied by domains aligned opposite to the field.

In this way the piece of material becomes magnetized.

Iron comes in two forms, hard and soft.  Hard and soft are term describing the magnetic properties of the material.  In hard iron the domains do not shift back into their random positions when the external field is removed.  In soft iron, the domains do shift back into their random positions when the external field is removed.  To make permanent magnets a piece of hard iron is placed into a magnetic field.  The domains align with the field, and they retain most of that alignment when the field is removed.  Soft iron is used as a core in electromagnets.  A wire is wound around an iron core.  A current flowing through the wire coil produces its own magnetic field and magnetizes the iron.  The magnetic field produced by the iron is much stronger than the field produced by the current in the coil.  Typically an iron core magnifies the field by a factor of 100 to 1000.  When the current in the coil is reduced to zero, the soft iron core loses its magnetization.

Magnetic effects are temperature sensitive.  At higher temperatures the atoms in the material have a higher average kinetic energy, and it is easier for interactions to misalign the spins.  Above a critical temperature known as the Curie temperature, ferromagnets lose their ferromagnetic properties.

#### Forces between magnets

Macroscopically, magnets act like current loops.  The internal currents of the electrons produce a net magnetization current flowing along the surface of the material.  (In the interior of the material currents flowing in opposite directions produce zero net current.)

In an external magnetic field produced by another magnet or by a current flowing in a wire, magnets are therefore acted on by forces and torques.  In a uniform external field, a current loop, and therefore a magnet, experiences no net force, but a net torque.  The torque tries to align the magnetic moment of the magnet with the external field.  The magnetic moment of a magnet points from its south pole to its north pole.

In a non-uniform magnetic field a current loop, and therefore a magnet, experiences a net force.

The force tries to pull an aligned dipole into regions where the magnitude of the magnetic field is larger and push an anti-aligned dipole into regions where magnitude the magnetic field is smaller.

If the magnetic field is pointing into the z-direction, the force on a magnetic dipole in that field is given by

Fz = μzdBz/dz.

When two bar magnets are brought together, unlike poles attract like poles repel.

 Link:  Levitron, the amazing anti-gravity top

#### The earth magnetic field

Near the surface of the earth magnets orient themselves so that their north poles point north.  In the magnetic field of the earth they experience a torque that tries to align them with the earth magnetic field.  The pattern of the field lines resembles that of a bar magnet.

Inside a bar magnet and near the center of the earth the magnetic field points from the magnetic south pole towards the magnetic north pole.  Outside the bar magnet and near the surface of the earth the magnetic field lines complete the loop from the magnetic north pole to the magnetic south pole.  Since the direction of the magnetic field near the earth surface is towards the north, the must be a magnetic south pole located near the geographic north pole, as shown in the diagram to the right.