Magnetism and ElectroMagnetism

Magnetism in Technology

Quick Definitions One charge Two Charges There is no “magnetic charge” Monopole Two Charges Dipole There is no “magnetic charge” “magnetic monopole”

Vector Products Dot Product Cross Product Vector x Vector = Scalar Vector x Vector = Vector Right-hand rule Non-Commutative

Quantum Origins While there is no magnetic charge that makes a particle “north” or “south”, every particle does have a magnetic dipole (north-south pair) Magnetic dipole called “spin” Note: nothing is actually ‘spinning’ ‘Spin’ is a fundamental property of matter

Types of Magnets Ferromagnetic Paramagnetic Diamagnetic Magnetic moments of unpaired electrons aligned in one direction Paramagnetic Random alignment due to thermal fluxuations Diamagnetic Align to counter an external magnetic field

Periodic Table

Ferromagnetism “Permanent Magnets” are a result of the energy structure of the incomplete 3d shell in some materials Unpaired spin in 3d shells with protective 4s orbitals

ElectroMagnetism Spin is one source of magnetism Moving charges also create a magnetic field that rotates around the axis of motion + + Electric Field Magnetic Field

3D Vector Convention Consider the field in and out of the page being shown with arrows (like bow-and-arrows) Coming toward you (Out of the page) Going away from you (Into of the page)

Fun Fact: Relativity Because magnetic fields are created by a moving charge, and movement is relative to your reference frame, magnetism is a result of relativity. This is why Einstein’s work in electrodynamics lead him to develop the Theory of Special Relativity

Electrodynamics If we consider a number of charges, we end up with a resultant magnetic field that looks like this Right Hand Rule: Thumb: Current Fingers: B-Field

Solenoids: Wire Coils Applying this rule, we can figure out what the magnetic field around a coil looks like.

Solenoids We can create a region of an aligned magnetic field.

Moving Charge in a B-Field Units of B-field: Tesla

Practice Problems Section Review Page 767, Questions 1-3

Deflection of a moving charge in a B-Field Length Contraction An object traveling relative to an observer will be shorter in the observers frame Time Dilation A clock travelling relative to an observer will measure time passing more slowly than in the observers frame.