p202c30: 1 Chapter30: Electromagnetic Induction Motional EMF’s Conductor Moving through a magnetic field Magnetic Force on charge carriers Accumulation of charge Balanced Electrostatic/Magnetic Forces qvB=qE Induced Potential Difference V = EL = vBL Generalized d V = v  B  dl F = qv  B

p202c30: 2 F = qv  B I With conduction rails: demonstrations with galvanometer moving conductor moving field!

p202c30: 3 I Consider circuit at right with total circuit resistance of 5 W, B =.2 T, speed of conductor = 10 m/s. Determine: (a) EMF, (b) current, (c) power dissipated, (d) magentic force on conducting bar, (e) mechanical force needed to maintain motion and (f) mechanical power necessary to maintain motion. d V = v  B  dl

p202c30: 4  B dl=dr I

p202c30: 5 Faraday’s Law of Induction Changing magnetic flux induces and EMF Lenz’s Law: The direction of any magnetic induction effect (induced current) is such as to oppose the cause producing it. (opposing change = inertia!)

p202c30: 6 A E B (increasing) A E B (decreasing) A E B (increasing) A E B (decreasing)

p202c30: 7 I Conducting rails: changing flux from changing area dA=l vdt

p202c30: 8 Simple Alternator B   t

p202c30: 9 Example: A coil of wire containing 500 circular loops with radius 4.00 cm is placed in a uniform magnetic field. The direction of the field is at an angle of 60 o with respect to the plane of the coil. The field is decreasing at a rate of.200 T/s. What is the magnitude of the induced emf? 60 o

p202c30: 10 A “new” lab experiment r I=I 0 sin(wt)  = B(r,t)

p202c30: 11 Eddy Currents Induced currents in bulk conductors magnetic forces on induced currents energy losses to resistance ex: Conducting disk rotating through a perpendicular magnetic field Ferromagnet ~ Iron (Electrical Conductor) Constrain Eddy currents with insulating laminations

p202c30: 12 Induced Electric Fields B (increasing) Changing magnetic Flux produces an EMF E Induced Electric Field E Not an Electrostatic field Not Conservative!

p202c30: 13 B increasing I I’ induced E I increasing

p202c30: 14 Maxwell’s Equations Lorentz Force Law

p202c30: 15 Superconductivity zero resistvity below T c (with no external magnetic field) with field above the critical field B c, no superconductivity at any temperature Superconducting Normal B T TcTc BcBc

p202c30: 16 More magnetic fun with superconductivity: the Meissner Effect Within a superconducting material, B inside = 0! magnetic field lines are expulsed from superconductor Relative permeability K m = 0 internal field is reduced to 0 => Superconductor is the perfect diamagnetic material!

p202c30: 17 mechanical effects ferromagnetic or paramagnetic marterials attracted to permanent magnet superconductor repels permanent magnet! Type-II superconductors small fillaments of “normal phase” coexist within bulk superconductor some magenetic field lines penetrate material two critical fields field just begins to penetrate material B c1 : magnetic field just begins to penetrate material B c2 :bulk material ”goes normal” more practical for electromagnets: higher T c and B c2