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Unformatted text preview: Magnetic fields in matter • All matters contain magnetic moments, either from the orbital motion of a charge particle (e.g. electron in an atom) or from the intrinsic properties of an elementary particle – the spin • There are three major kinds of magnetic response of matters : diamagnetism, paramagnetism and ferromagnetism • We really need quantum mechanics to properly understand magnetism in matters. Here, we will give a simple classical (i.e. not quite correct) discussion of the phenomena of paramagnetism and diamagnetism First, if a magnetic dipole is placed under a magnetic field, the dipole would experience a torque. Consider a square loop of sides a and b with a current I under a magnetic field z B ˆ B = : Force on one side = ± BIb y ˆ Torque = F r × = x ˆ ) sin )( ( θ 2 a BIb 2 = x ˆ sin θ BIab = x ˆ sin θ Bm m = Iab = dipole moment ∴ In general, B m τ × = (6.1) • The magnetic dipole will be aligned and pointed to the same direction as the Bfield. So the dipole moment along the Bfield direction increases with the increase of B. This is called a paramagnetic response. • This can be compared to the case of electrostatics, where the torque E p τ × = also tends to align the electric dipole to an orientation parallel to the applied electric field. Note that it is called dielectric response in electrostatics. • Diamagnetic response is different : the magnetic moment along the Bfield direction would decrease as the Bfield increases In a classical picture of an orbiting electron : m = (area) × (current) z ˆ current = time charge R 2 ev R 2 qv v R 2 q π π π = = = / ∴ m = z z ˆ ˆ ) ( 2 evR R 2 ev R 2 =  π π The orbital motion is due to attractive electric force : R v m R e 4 1 2 e 2 2 = πε If a Bfield is applied along the zaxis, it requires (assuming the same radius of orbit) R v m Bev R e 4 1 2 e 2 2 ' ' = + πε So that the new velocity will become bigger : e 2 2 m R Bev v v ) ' ( ' = e e m 2 BeR v 2 1 m R Bev v v = 2245 ' ' ' The magnetic dipole moment, which points to the negative z direction, will increase in magnitude. Correspondingly, if the electron is orbiting at an opposite direction with m pointing along z ˆ , application of a Bfield along z ˆ will decrease the orbital speed and decrease the magnitude of m . So, if initially we have a pair of oppositely orbiting electrons, the net dipole moment is zero. Application of a Bfield will induce a net magnetic dipole moment that is opposite to the direction of B. This is the classical picture for the mechanism responsible for diamagnetism. • Ferromagnetic materials, like paramagnetic materials, response in such a way that the magnetic dipole moment increase with the Bfield. They are different in two major aspects, first, ferromagnetism is highly nonlinear, so that ferromagnetic response is much, much stronger . Second, ferromagnetism can be retained even in the absent of an external Bfield....
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 Spring '10
 DrKwong
 Charge, Electrostatics, Magnetic Field, dipole moment

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