1 Magnets Magnet; an object that  Attract certain types of material, like iron.  Attract or repel another magnet.  All magnets have two poles, named the “north pole” and the “south pole”. The reason for the poles are called north or south is because the Earth is a gigantic magnet with its magnetic south pole is close to its geographicnorth pole, and its magnetic north pole is close to its geographic south pole. When a magnet is let to move freely, it will align itself with its north pole pointing to the north. This is how a magnetic compass works. A magnetic monopole has never been found. It is proposed by Paul Dirac in 1931 to explain electron charge quantization. Searching for magnetic monopole is active and in the frontier of physics research.

2 Magnetic fields Magnetic field is introduced to explain the fact that magnetic forces act over distance.  Magnetic field lines illustrate the magnetic field.  Outside the magnet, the field lines start from the north pole, ends at the south pole. Inside the magnet, the field lines continue from the south pole to the north pole to complete a loop.  The field direction is tangent to the field line. No field lines cross.  The density of the field lines illustrates the field strength.  Unit: teslas, T. Magnet was first found in nature (the lodestone) and the Chinese first used it as a compass ~200 BC. Can you use a compass in the polar areas?

3 Magnetic fields and moving charges Magnetic field exerts force on moving charges: Vector cross product, the result vector direction follows the right hand rule. This force does NOT do work to the charge particle.

4 Example: particle velocity selector Used in many (medical) cyclotron facilities to select the right momentum (velocity) of particles:

5 Example: particle momentum measurement Charge particles with an initial velocity perpendicular to the B field move in a circles in a magnetic field. The radius: The period:

6 When the initial particle velocity is not perpendicular to the B-field The general case: helical particle motion in magnet fields: Auroras

7 Example: mass spectrometer of charged particles Mass spectrometers are used to determine the masses of atoms or molecules, or their relative abundance in a sample.

8 The Hall Effect, a measure on the magnetic field The Hall Effect: A magnetic field deflects electrons in a current- carrying strip. In 1879, Edwin Hall, a graduate student in physics, used a magnetic field to manipulate the charge carriers in a strip of gold foil. Hall showed that the current in the foil was the result of negative charges in motion. He received a professorship for this experiment. By measuring ΔV and I, we know B.

9 Derive of the formula for Hall effect

10 Magnetic force on current-carrying wire If magnetic field exerts forces on moving charges, it should also exert a force on a current-carrying wire.

11 Torque on a loop of current, and the magnetic dipole moment Electric Motors: torque on a loop of current in magnetic fields. When we define a magnetic dipole moment as: Then the torque becomes: A is the area of the loop, a vector. When the loop has N turns:

12 Potential energy in a B-field A magnet (or a current-carrying wire loop) has potential energy in a magnetic field: Some atoms also have magnetic dipole moments. An external magnetic field will exert torque on them, causing them to align with it. This is the basis for the MRI (magnetic resonance imaging) machine, a technology used in hospitals to image the interior of the human body.