§5.1: Magnetic Field

Christopher CrawfordPHY 417

2015-01-16

Outline• Magnetic field and torque

William Gilbert – field lines of permanent magnets Hans Christian Ørsted – magnetic field of a current

• MagnetostaticsAndré-Marie Ampère – force on two straight wiresCurrent element – continuity equation

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Static force lawsElectrostatics – 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

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History of magnetism• The magnetic force was known in antiquity

– Magnetism more predominant in nature but more difficult to quantify:1. Permanent magnets (magnetization), not electric currents2. No magnetic (point) charge (monopole) –> dipole effect (N,S poles)3. 1-d currents instead of 0-d charges –> can’t split a wire!4. 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

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Early magnetismhttps://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”

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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

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• Magnetic field lines look like an electric dipole (in fact the magnetic dipole was discovered first!)

Iron Filings

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Iron Filings

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Difference between E, B dipoles• Same as the differences between Flux and Flow!

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• 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”

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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

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

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Electrodynamics• André-Marie Ampère showed that parallel currents attract

and antiparallel currents repel

• The magnetic force is the basis for electromagnetic units

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Ampère’s generalization• Experimental laws:

• Force formula

• Problem– The force between two current elements does NOT

point along the line from the one to the other!

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Peer criticism

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MAX

WEL

LH

EAVI

SID

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Current elements• Analogous to charge elements – different dimensions

• Relations between charge / current and different dimensions – analogy: multi-lane highway – current flux

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

• 4-vector current

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