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# Ch6 - Magnetic fields in matter • All matters contain...

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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 B-field. So the dipole moment along the B-field 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 B-field direction would decrease as the B-field 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 B-field is applied along the z-axis, 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 B-field 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 B-field 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 B-field. 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 B-field....
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Ch6 - Magnetic fields in matter • All matters contain...

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