Magnetic field for a straight line o o Approximation for an infinite wire x L Ampere s Law o Rules for amperes law L must be a closed loop Only current enclosed by the loop counts in Ampere s law Current can be positive or negative depending on flow If current flows along thumb when magnetic field goes along curling fingers it is positive right hand rule o Example Ring of current o o o Example Infinite Cylinder of radius a carrying a uniform current I o o o o o o Infinite solenoid o Magnetic field outside is ZERO Magnetic Force Net work done by a magnet is ZERO A point charge confined to a magnetic field o Special cases o o Hall Effect o o o Note V a is voltage on the battery o o For a straight finite wire Example o o Faraday s Law o o Since there is no magnetic force in the case where the magnetic field is moving there is an effective electric field Magnetic Flux o o Example o o Resistive Force The amount of work required to keep the loop moving at a constant velocity v o o Example o o Note the electric field causes a current to run clockwise so a magnetic field is created to oppose the magnetic field on the solenoid I which is counter clockwise o o o Magnetic Properties 1 paramagnetic materials o Develop an induced weak dipole moment parallel to applied magnetic field o Weakly attractive o Occurs in systems with an unpaired electron Net magnetic moments due to pairs of electrons tend to cancel each other electrons in atoms behave like tiny current loops If an atom has an unpaired electron o The electron spinning implies that there is a dipole moment and the electron s orbital motion cause a net magnetic moment o 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 o develop an induced weak dipole moment anti parallel to o 2 Diamagnetic applied magnetic field o weakly repulsive o Paired up electrons o 3 Ferromagnetic Therefore Diamagnetic is a weak repulsion o develop a net dipole moment due to atomic alignments even in the absence of applied magnetic field o strongly attractive o 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 figure Aligning the dipoles together as in the following The alignment only occurs below the cuvic temperature Alignment is uniform over discrete patches called domains Magnetization of ferromagnetic material is associated with motion of domain boundaries in presence of external magnetic field 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 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 Magnetization o o Inductance Magnetic flux N is the number of loops o o o Inductance for a solenoid of length l and cross sectional area A Energy in an inductor Not on any of the first three exams Charging an Inductor Resistor Circuit Discharging an Inductor Resistor Circuit Energy as a function of time The energy lost is dissipated as heat in the resistor o Power and energy used by the resistor o Inductor Capacitor Circuits oscillators
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