3 Magnetic Flux, F: The number of magnetic (flux) field lines which pass through a given cross-sectional area AUnits:F webersB TeslaA area m2angle formed between B and the normal to the loop (area vector A)The area vector A is perpendicular to the surface A and has a magnitude equal to the area A.
9 Gauss’ Law in Magnetism Magnetic fields do not begin or end at any pointThe number of lines entering a surface equals the number of lines leaving the surfaceGauss’ law in magnetism says:
10 Ampere’s Law – General Form Also known as the Ampere-Maxwell lawWhere is the electric flux.The second term Id is called displacement current and is caused by electric fields that vary with time as in a capacitor.
11 Example: Capacitor Consider surfaces S 1 and S2 . The current through S1 is I.There is no conducting current through S2The electric flux throughS2 is EAA is the area of the capacitor platesE is the electric field between the platesIf q is the charge on the plate at any time, FE = EA = q/eo
12 Example: Capacitor cont’d The displacement current isThe displacement current is the same as the conduction current through S1The displacement current on S2 is the source of the magnetic field on the surface boundary
13 Magnetic fields are produced both by conduction currents and by time-varying electric fields
14 Classification of Magnetic Substances Paramagnetic and ferromagnetic materials are made of atoms that have permanent magnetic momentsDiamagnetic materials are those made of atoms that do not have permanent magnetic moments
15 Classifying Materials by Permeability Materials can be classified by how their permeability compares with the permeability of free space (mo)Paramagnetic: mm > moDiamagnetic: mm < mo
16 Examples of Ferromagnetic Materials ironcobaltnickelgadoliniumdysprosium
17 DomainsThe domain is an area in a material within which all magnetic moments are aligned
18 Domains, Unmagnetized Material The magnetic moments in the domains are randomly alignedThe net magnetic moment is zero
20 Meissner EffectCertain types of superconductors also exhibit perfect diamagnetismThis is called the Meissner effectIf a permanent magnet is brought near a superconductor, the two objects repel each other
21 Earth’s Magnetic Field Like a bar magnetThe Earth’s south magnetic pole is located near the north geographic poleThe Earth’s north magnetic pole is located near the south geographic poleMagnetic Declination
22 Dip Angle of Earth’s Magnetic Field If a compass is free to rotate vertically as well as horizontally, it points to the Earth’s surfaceThe angle between the horizontal and the direction of the magnetic field is called the dip angleThe farther north the device is moved, the farther from horizontal the compass needle would beThe compass needle would be horizontal at the equator and the dip angle would be 0°The compass needle would point straight down at the south magnetic pole and the dip angle would be 90°
23 Reversals of the Earth’s Magnetic Field The direction of the Earth’s magnetic field reverses every few million yearsEvidence of these reversals are found in basalts resulting from volcanic activityThe origin of the reversals is not understood
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