Magnetization

Diamagnetism occurs in substances where magnetic moments inside atoms all cancel out, the net magnetic moment of the atom is zero. The induced magnetic moment is directed opposite to the applied field. Diamagnetism is weakly dependent on T. Diamagnetic (induced atomic moment) effect is overcome in paramagnetic materials, whose atoms have uncompensated magnetic moments. These moments align with the applied field to enhance the latter. Temperature T wants to destroy alignment, hence a strong (1/T) dependence. Magnetic effects are a completely quantum-mechanical phenomenon, although some classical physics arguments can be made.

Example: Magnetic dipoles in a paramagnetic material Nitric oxide (NO) is a paramagnetic compound. Its molecules have maximum magnetic moment of ~  . In a magnetic field B=1.5 Tesla, compare the interaction energy of the magnetic moments with the field to the average translational kinetic energy of the molecules at T=300 K.

Ferromagnetism Alignment of magnetic domains in applied field In ferromagnetic materials, in addition to atoms having uncompensated magnetic moments, these moments strongly interact between themselves. Strongly nonlinear behavior with remnant magnetization left when the applied field is lifted. Permeability K m is much larger, ~1,000 to 100,000

Hysteresis and Permanent Magnets Magnetization value depends on the “history” of applied magnetic field Magnetization curve for soft iron showing hysteresis Example: A ferromagnetic material A permanent magnet is made of a ferromagnetic material with a M~10 6 A/m The magnet is in the shape of a cube of side 2 cm. Find magnetic dipole moment of a magnet. Estimate the magnetic field at a point 10 cm away on the axis

Experiments leading to Faraday’s Law Electromagnetic Induction – Time-varying magnetic field creates electric field

Changing Magnetic Flux No current in the electromagnet – B=0 - galvanometer shows no current. When magnet is turned on – momentarily current appears as B increases. When B reaches steady value – current disappears no matter how strong B field is. If we squeeze the coil as to change its area – current appears but only while we are deforming the coil. If we rotate the coil, current appears but only while we are rotating it. If we start displacing the coil out of the magnetic field – current appears while the coil is in motion. If we decrease/increase the number of loops in the coil – current appears during winding/unwinding of the turns. If we turn off the magnet – current appears while the magnetic field is being disappearing The faster we carry out all those changes - the greater the current is.

Faraday’s Law quantified

Emf and Current Induced in a Loop If the loop is made of the insulator, induced emf is still the same But the resistance is large, so little (or no current) is flowing

Circuit with induced EMF only A 1 B 1 A 2 B 2 I 1 – I 3 I1I1 I3I3 R1R1 R2R2 R3R3 Kirchhoff’s rules still apply! It is only the origin of the EMFs that is different here from ordinary batteries.

Direction of the induced EMF

Alternating current (ac) generators

Direct current (dc) generators Split ring (commutator) does the job of reversing polarity every half cycle

Motional emf – conductor moving in a constant magnetic field

Generators as Energy Converters Generator does not produce electric energy out of nowhere – it is supplied by whatever entity that keeps the rod moving. All it does is to convert it to a different form, namely to electric energy (current)

Motion does not necessarily mean changing magnetic flux!

Significance of the minus sign – Lenz’s Law Induced current has such direction that its own flux opposes the change of the external magnetic flux Magnetic field of the induced current wants to decrease the total flux Magnetic field of the induced current wants to increase the total flux Correspondingly, magnetic forces oppose the motion – consistently with conservation of energy! Lenz’s Law – the direction of any magnetic induction effect as to oppose the cause of the effect Lenz’s Law – a direct consequence of the energy conservation principle

Finding the direction of the induced current

Induced Electric Fields