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2. Electromagnetism and

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

electromagnetic induction

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2.1 Magnetic flux

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

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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.

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Magnetic field patterns :

Unlike poles-Attraction Like poles-Repulsion

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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)

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Magnetic Flux

Number of lines of magnetic force coming out or entering into a magnetic surface.

Symbol: Unit: weber (Wb)

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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)

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2.3 mmf (magnetomotive force)

The force - produces the magnetic field F = I*N ampere turn Symbol: FUnit : AT

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2.4 Field strength (H) &

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

Permeability

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

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• 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

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Permeability of Free Space • magnetic space constant - permeability of

vacuum or of air.

• symbol: o Unit: T/(A/m) Or H/mm

• value: 4xx10-7 H/m Relative and Absolute Permeability

• Absolute permeability = o x relative permeability = o x r

• where r = relative permeability

• symbol: r unit: none

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Ferromagnetic materialsr1

• 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

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Diamagnetic materialsr 1

• e.g. gold, silver.

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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 F

lux density

Fig. 6

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2.6 Faraday’s Law

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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.

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2.7 Faraday’s law of

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.

Electromagnetic Induction

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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.

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2.9 Fleming’s left and Right-

Fleming’s right-hand rule

hand Rules

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Fleming’s left-hand rule

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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)

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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).

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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 =