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Unformatted text preview: 1 In this chapter we will discuss the following topics: Gauss’ law for magnetic field The missing term from Ampere’s law added by Maxwell The magnetic field of the earth Orbital and spin magnetic moment of the electron Diamagnetic materials Paramagnetic materials Ferromagnetic materials Chapter 32: Maxwell’s equations; Magnetism in matter Maxwell’s equations; Magnetism in matter 2 Fig.a Fig.b Gauss’ Law for Magnetic Fields Gauss’ Law for Magnetic Fields In electrostatics we saw that positive and negative charges can be separated . This is not the case with magnetic poles: If we attempt to cut the magnet into pieces, we do not get isolated north and south poles separately . Not even if we break the magnet down to its individual atoms and then to its electrons and nuclei, will we be able to produce magnetic monopole. Thus: The simplest magnetic structure that can exist is a magnetic dipole. Magnetic monopoles do not exist (as far as we know). 3 Magnetic Flux B B dA Φ ≡ ⋅ ∫ ur ur Gauss’s Law in Magnetism Gauss’s Law in Magnetism: Statement that no magnetic monopoles appear to exist. o enc B dA Recall the Gauss's Law for electrostatics E dA q ⋅ = ⋅ = ε ∫ ∫ Ñ Ñ 4 Maxwell’s Equations?? Maxwell’s Equations?? o B o Q E dA B dA d E ds dt B ds I ⋅ = ε ⋅ = Φ ⋅ =  ⋅ = μ ∫ ∫ ∫ ∫ Ñ Ñ Ñ Ñ Gauss’ Law for Electric Fields Gauss’ Law for Magnetic Fields Faraday’s Law , induced Electric Field from changing magnetic flux Ampere’s Law Who is Maxwell and are these his equations??? 5 Displacement Current: Generalize Ampere’s Law ( 29 E d o E o d o o o d I dt d B ds I I I dt Φ ≡ ε Φ ⋅ = μ + = μ + μ ε ∫ Ñ The problem : Ampere’s Law states that the integral of the magnetic field about a closed curve is equal to the current passing through ANY surface bounded by that curve. As seen in the figure, one suface has a net transfer of charge, the other does not, thus one integration will give you a B field, the other does not. CONTRADICTION Maxwell added a new term to Ampere’s Law that resolved the contradiction, the displacement current term, I d ! 6 PROBLEM WITH AMPERE’S LAW??? PROBLEM WITH AMPERE’S LAW??? Induced Magnetic Fields Induced Magnetic Fields According to Faraday’s law of induction, changing magnetic flux induces an electric field : ∫ = ⋅ dt dΦ s d E B r r Using a symmetry argument, J.C. Maxwell guessed that, the similar statement can be also made about changing electric flux: ∫ = ⋅ dt dΦ ε μ s d B E r r In both equations, the integral is taken along a closed loop . Changing electric flux induces a magnetic field. This is mathematically given by Maxwell’s law of induction : 7 Contradiction removed! More over this new term shows… Magnetic fields are produced both by conduction currents and by timevarying electric fields....
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This note was uploaded on 10/10/2010 for the course PHY 108 taught by Professor Iashvili during the Spring '08 term at SUNY Buffalo.
 Spring '08
 IASHVILI
 Physics, Magnetism

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