Christopher Crawford PHY

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Presentation transcript:

Christopher Crawford PHY 311 2014-03-28 §5.1: Magnetic fields Christopher Crawford PHY 311 2014-03-28

Outline Introduction to magnetism History of magnetism Magnetic fields Review: current Lorentz force

Magnetic scalar potential Electrostatics – Coulomb’s law Magnetostatics – Biot-Savart law Geometrical Gauss -> Ampere’s law U interpretation as boundary currents Statement in terms of boundary conditions Technique for calculating coils B.C.’s: Flux lines bounded by charge Flux lines continuous Flow sheets continuous (equipotentials) Flow sheets bounded by current

Equations of Electrodynamics

History of magnetism The magnetic force was known in antiquity Magnetism more predominant in nature but more difficult to quantify: Permanent magnets (magnetization), not electric currents No magnetic (point) charge (monopole) –> dipole effect (N,S poles) 1-d currents instead of 0-d charges –> can’t split a wire! Static electricity produced in the lab long before steady currents Timeline (from “A Ridiculous Brief History of Electricity and Magnetism”) 600 BC 1200 AD 1259 AD 1600 AD 1742 AD 1820 AD 1820 AD 1820 AD 600 BC Thales of Miletus discovers lodestone’s attraction to iron 1200 AD Chinese use lodestone compass for navigation 1259 AD Petrus Peregrinus (Italy) discovers the same thing 1600 AD William Gilbert discovers that the Earth is a giant magnet 1742 AD Thomas LeSeur shows inverse cube law for magnets 1820 AD Hans Christian Ørsted discovers that current twists magnets Andre Marie Ampere shows that parallel currents attract/repel Jean-Baptiste Biot & Felix Savart show inverse square law

Magnetic fields In magnetism it is more natural to start with the concept of “Magnetic field” than the actual force law! (dipole) Compass aligns with B-field Iron filings line up along magnetic field lines Magnetic field lines look like an electric dipole (in fact the magnetic dipole was discovered first!)

Difference between E, B dipoles Same as the differences between Flux and Flow! Charge = sources of flux Conservative flow [potential] Example: Amber (electric) Rub to charge 2 charges (+/–) “monopole fluids” Exerts force on charges Continuous field lines [flux] Rotational (source of flow?) Example: Lodestone (magnet) Always charged 2 poles (N/S) “inseparable dipole” Exerts torque on other magnets

First connection to currents: from Wittaker, “A history of the theories of Aether and Electricity”

The current connection There is no magnetic monopole – N/S cannot be separated The source of all magnetism is electric current A dipole is just a current loop Hans Christian Ørsted Current produces B-field Quantified by Biot & Savart

Hans Christian Ørsted: from Wittaker, “A history of the theories of Aether and Electricity”

Electrodynamics Andre Marie Ampere shows that parallel currents attract and antiparallel currents repel The magnetic force is the basis for electromagnetic units

Current elements Analogous to charge elements – different dimensions Relations between charge / current and different dimensions – analogy: multi-lane highway – current flux

Continuity equation Local conservation of charge Current I is a flux; current density J = flux density 4-vector current

Lorentz force