electromagnetic induction 2. Electromagnetism and electromagnetic induction 2.1 Magnetic flux 2.2 Flux density 2.3 mmf 2.4 Field strength (H) & Permeability 2.5 B/H curves 2.6 Faraday’s Law 2.7 Faraday‘s law of Electromagnetic Induction 2.8 Lenz’s Law 2.9 Fleming’s Left-hand and Right-hand Rules 2.10 Self-inductance 2.11 Energy stored

Magnetic field is invisible-observed by using paper and iron fillings. 2.1 Magnetic flux Magnetic field is invisible-observed by using paper and iron fillings.

Line of magnetic flux (lines of magnetic force). North-seeking pole or N-pole points towards north. South-seeking pole or S-pole points towards south.

Magnetic field patterns : Unlike poles-Attraction Like poles-Repulsion

Characteristic of lines of magnetic flux Line of magnetic flux - direction, closed loop Shorten lines of magnetic flux (unlike poles attract each other) Parallel in same direction repel one another (like poles repel each other)

Magnetic Flux Number of lines of magnetic force coming out or entering into a magnetic surface. Symbol:  Unit: weber (Wb)

2.2 Flux density magnetic flux entering unit area normally (at right angle) is the magnetic flux density Symbol: B Unit: tesla (T) Flux density B= /A tesla (T)

2.3 mmf (magnetomotive force) The force - produces the magnetic field F = I*N ampere turn Symbol: F Unit : AT

2.4 Field strength (H) & Permeability Field Strength magnetic field intensity - m.m.f. per unit length of the magnetic circuit. Magnetic intensity = F/l = IN/l Symbol: H Unit: ampere per metre known as magnetizing force OR magnetic field strength

Magnetic field is concentrated in the iron rod. Brass rod has little effect on the magnetic field.

Iron has a lower “magnetic resistance” than that of the surrounding air path. Magnetic resistance of the brass has much the same value of the surround air. Every material has particular value of conductivity known as magnetic permeability. Flux Density = absolute permeability x magnetic field intensity B = H Symbol:  Unit: T/(A/m) OR H/m

Permeability of Free Space magnetic space constant - permeability of vacuum or of air. symbol: o Unit: T/(A/m) Or H/mm value: 4xx10-7 H/m Relative and Absolute Permeability Absolute permeability = o x relative permeability  = o x r where r = relative permeability symbol: r unit: none

Ferromagnetic materials e.g. iron, steel, nickel and cobalt Paramagnetic materials r 1 i.e. material become weakly magnetized in the direction of the magnetising field. e.g. aluminium, chromium

Diamagnetic materials e.g. gold, silver.

2.5 B/H curves Magnetization characteristics of soft magnetic materials Flux density increases rapidly due to alignment of a large number of magnetic domains Knee point –further increase of H causes very little change in magnetic field. magnetic saturation - all domains aligned with the magnetic field. Magnetic field intensity H B Flux density Fig. 6

2.6 Faraday’s Law

an e.m.f. is induced in the conductor whenever it cuts line of magnetic flux. Conductor move upwards or downwards - induced e.m.f. is zero. Conductor’s velocity will affect the magnitude of the induced e.m.f.

Electromagnetic Induction 2.7 Faraday’s law of Electromagnetic Induction Magnetic field linking with the conductor changes - e.m.f. is induced. Induced e.m.f.’s magnitude rate of change of the magnetic flux linking with the conductor.

2.8 Lenz’s Law The e.m.f. induced - circulate current in a direction opposes the change of magnetic flux inducing the e.m.f.

2.9 Fleming’s left and Right- hand Rules Fleming’s right-hand rule

Fleming’s left-hand rule

2.10 Self-inductance Conductor carrying current is surrounded by magnetic field. Conductor current  , magnetic field  . By Lenz‘s Law,  in flux  e.m.f. to be induced in conductor opposes the change in flux (change in current). This e.m.f. is Self-induced e.m.f. (self-inductance)

Self-inductance of 1 henry (H) if - e. m. f Self-inductance of 1 henry (H) if - e.m.f. of 1 volt (V) is induced when current changes at 1 ampere per second (A/s).

2.11 Energy Stored In a circuit of inductance L henrys. Current increases at a uniform rate from zero to I amperes in t seconds. Average current in the circuit is I/2 amperes, Average value of induced e.m.f. is L*(rate of change of current)=LI/t The average energy consumed by the inductance is therefore: W = Eit =