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Unformatted text preview: Chapter 32 Maxwells equations Magnetism in matter Will cover the following topics Gauss law for magnetic field The missing term from Amperes law added by Maxwell 1 The magnetic field of the Earth Orbital and spin magnetic moment of the electron Diamagnetic materials Paramagnetic materials Ferromagnetic materials Lets say we have a permanent bar magnet with well defined north and south poles. If we attempt to cut the magnet into pieces, we do not get isolated orth and south poles separately. Gauss Law for Magnetic Fields In electrostatics the positive and negative charges can be separated This is not the case with magnetic poles: 2 north and south poles separately. Instead, we get again magnetic dipoles. 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) Gauss law for magnetic field is a formal way of saying that magnetic monopoles do not exist: the net magnetic flux through any closed surface is zero: = = A d B B r r We can compare this equation to the Gauss law for electric field: = = q A d E enc E r r Gauss Law for Magnetic Fields (contd) 3 Gauss law for the electric field says that the integral is proportional to the net enclosed charge q enc Gauss law for the magnetic field says that there is no net magnetic flux through the surface, because there can be no magnetic charge enclosed. The simplest magnetic structure that can exist is a dipole, which consists of both, a north and south poles. Thus there must always be as much magnetic flux into the surface as out of it, producing zero net magnetic flux In both equations, the integral is taken over closed Gaussian surface According to Faradays law of induction, changing magnetic flux induces an electric field:  = dt d 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: Induced Magnetic Fields 4 = dt d 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 Maxwells law of induction: Thus, according to Maxwells law of induction, changing electric flux induces a magnetic field: Example demonstrating Maxwells law of induction: h Consider a parallelplate capacitor with circular plates as shown in the figure Induced Magnetic Fields (contd) = dt d s d B E r r 5 h The charge on the capacitor is being increased at a steady rate by a constant current i . As a result, the electric field between the plates also increases at a steady rate h The bottom figure is a view of righthand plate....
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 Fall '08
 Staff
 Magnetism

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