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§5.1: Magnetic Field

§5.1: Magnetic Field. Christopher Crawford PHY 417 2015-01-16. Outline. Magnetic field and torque William Gilbert – field lines of permanent magnets Hans Christian Ørsted – magnetic field of a current Magnetostatics André-Marie Ampère – force on two straight wires

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§5.1: Magnetic Field

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  1. §5.1: Magnetic Field Christopher Crawford PHY 417 2015-01-16

  2. Outline • Magnetic field and torque William Gilbert – field lines of permanent magnets Hans Christian Ørsted – magnetic field of a current • Magnetostatics André-Marie Ampère – force on two straight wires Current element – continuity equation

  3. Static force laws Electrostatics – Coulomb’s law Magnetostatics – Biot-Savart law B.C.’s:Flux lines bounded by charge Flux lines continuous Flow sheets continuous (equipotentials) Flow sheets bounded by current

  4. 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 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

  5. Early magnetism https://www.tcd.ie/Physics/Magnetism/Guide/compass.php • Wu Ching Tsung Yao (1040) • First mention of the magnetic compass • Petrus Perigrinus (1269) • “Epostolia de Magnete” – rediscovered it • William Gilbert (1600) • “De Magnete” – the earth is a magnet • René Descartes • effluvia of "threaded parts”

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

  7. Iron Filings

  8. Iron Filings

  9. 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

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

  11. 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

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

  13. Electrodynamics • André-Marie Ampère showed that parallel currents attractand antiparallel currents repel • The magnetic force is the basis for electromagnetic units

  14. Ampère’s generalization • Experimental laws: • Force formula • Problem • The force between two current elements does NOTpoint along the line from the one to the other!

  15. Peer criticism MAXWELL HEAVISIDE

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

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

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