Understanding the Link Between Electric Current and Magnetism - Prof. Andrew Lyke, Study notes of Electrical and Electronics Engineering

Download Understanding the Link Between Electric Current and Magnetism - Prof. Andrew Lyke and more Study notes Electrical and Electronics Engineering in PDF only on Docsity! Andy Lyke - SPSU 1 ECET 3500 Magnetism Andy Lyke - SPSU 2 ECET 3500 Magnetic fields ●Electric current (I) creates Magneto Motive Force (MMF) symbol is H units are Ampere-turns/meter I H Andy Lyke - SPSU 5 ECET 3500 Practical Electromagnets I H I H H Andy Lyke - SPSU 6 ECET 3500 Practical Electromagnets Andy Lyke - SPSU 7 ECET 3500 Practical Electromagnets Andy Lyke - SPSU 10 ECET 3500 From Hubert-Electric Machines Andy Lyke - SPSU 11 ECET 3500 Magnetic Induction E g=− d  dt =B⋅A For reasonable geometries : =|B|⋅|A|cos Andy Lyke - SPSU 12 ECET 3500 Magnetic Induction ●Therefore, we can induce a potential difference by changing B, A or Θ ●Another view is the “speed Voltage” –E is the generated potential difference along a straight wire of length l moving with velocity v through a magnetic field of flux density B –And v is the velocity component normal to B E=Blv Andy Lyke - SPSU 15 ECET 3500 For each cycle around the B-H loop, there is energy loss proportional to the area of the loop the loss per cycle increases as the peak value of B (therefore H) increases, resulting in more area within the loop. Empirically, it is found that the energy lost per cycle is proportional to a power of B, which is 1.6 for steel used in machinery Since the energy lost is a function of the area of the loop, the power loss is proportional to frequency. PHysteresis∝B peak 1.6 PHysteresis=K h⋅f⋅B peak 1.6 Hysteresis Andy Lyke - SPSU 16 ECET 3500 Driving a Core into Saturation 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 0 0.2 0.4 0.6 0.8 1 1.2 Flux Density vs. MMF(B-H curve) Magneto Motive Force (MMF) Fl ux D en si ty Andy Lyke - SPSU 17 ECET 3500 Driving a Core into Saturation ●Up to about B=0.8, the B vs H curve is somewhat linear ●Above B=0.1, very much more H is required to achieve small increases in B, so the magnetizing current must increase disproportionately to achieve further incremental changes in B Andy Lyke - SPSU 20 ECET 3500 Driving a Core into Saturation •MMF is clearly not sinusoidal High order harmonics abound as incremental magnetizing current increases -1.5 -1 -0.5 0 0.5 1 1.5 -1.5 -1 -0.5 0 0.5 1 1.5 B vs Magnetizing Current, core saturating Ap*Sin(T) H Time B Andy Lyke - SPSU 21 ECET 3500 Electromagnetic Force •Force on a charge moving in a magnetic field •Cathode ray tube: F=qv×B q v Andy Lyke - SPSU 22 ECET 3500 Force on Current Carrying Conductor x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x f =qv×B f =l eff i ×B f i “Speed Voltage” ECET 3500 25 = bebe me i es li ait sat = ~ IPL | S INNS “ “7 _ ~ 5 SS nO, Hk =H Andy Lyke - SPSU  Andy Lyke - SPSU 26 ECET 3500 Magnetic Circuit •Battery drives current, limited by the wire's resistance •MMF=F=nI (current times turns) •H = F/l Ampere turns/meter Φ l=”mean length” (meters) Andy Lyke - SPSU 27 ECET 3500 Isotropic Core of Constant Cross Section •A = core cross section •Isotropic – µ is everywhere the same (in all directions) Φ l=”mean length” (meters) B= H =B×A