Magnetic properties of matter 10 20 14 9 18 AM 1 paramagnetic materials magnetic field Develop an induced weak dipole moment parallel to applied Weakly attractive Occurs in systems with an unpaired electron Net magnetic moments due to pairs of electrons tend to cancel each other o electrons in atoms behave like tiny current loops o If an atom has an unpaired electron The electron spinning implies that there is a dipole moment and the electron s orbital motion cause a net magnetic moment The following diagram shows the weakly attractive force although the external magnetic field is trying to line up the electrons with the magnetic field there may be bonding between atoms because there is a net dipole moment and heat will cause motion develop an induced weak dipole moment anti parallel to applied 2 Diamagnetic magnetic field weakly repulsive Paired up electrons o Therefore Diamagnetic is a weak repulsion 3 Ferromagnetic develop a net dipole moment due to atomic alignments even in the absence of applied magnetic field strongly attractive In sum Paramagnetism caused by aligning dipoles to magnetic field o Diamagnetism caused by slowing or speeding up an object in orbit o Magnetization Net magnetic dipole moment per unit volume o Chi m magnetic susceptibility Example Consider a cylinder of uniform magnetization what is the magnetic field due to this magnetization o Zoom in on the cross section o If magnetism was generated by an external magnetic field what is the net field inside the material o o Total magnetic field inside the magnetic material Paramagnetic example Magnetic susceptibility is positive if the material is paramagnetic Magnetic susceptibility is negative if the material is diamagnetic Diamagnetic example Ferromagnetic Fe Ni Co Characterized by spontaneous parallel arrangement of atomic moments even in the absence of external magnetic field Alignment caused by exchange forces quantum mechanical origin o Aligning the dipoles together as in the following figure o The alignment only occurs below the cuvic temperature Alignment is uniform over discrete patches called domains o Magnetization of ferromagnetic material is associated with motion of domain boundaries in presence of external magnetic field o When you put it in the external field the domains changed the domains aligned parallel to magnetic field grow at the expense of the other domains o Nonlinearity and hysteresis lag in the response of the material associated with the irreversibility of the domain wall motion why you can permanently magnetize objects o o Exam three Chapters 27 28 and 29 Index card allowed Faraday bio savart Lorenz 10 20 14 9 18 AM Inductance 10 20 14 9 18 AM Reminder of capacitor Current carrying circuits are associated with a quantity called inductance L L magnetic flux through circuit per unit current flowing through it o Units of inductance are Volts seconds Ampere Henry o In the above it is the same current that produces the magnetic field so it is the self inductance o Mutual inductance M Self inductance Solenoid of length l and cross sectional area A find inductance L Fill the solenoid with a magnetic material of permeability k m o Note inductance given by the above only if the material is everywhere where the magnetic field was Typically for inductors we use k m 1 so L L vac For ferromagnetic substances k m 10 3 or 10 4 so L 10 3 L vac Energy stored in an inductor o Therefore we can say that energy is stored in magnetic field Circuits RL and RLC circuits
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