Materi Fisika Listrik 7 Induksi Magnet

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– Magnetic flux– Induced emf

• Faraday’s Law• Lenz’s Law• Motional emf

– Magnetic energy– Inductance– Generators and transformers

Electromagnetic Induction

3 Things Required toGenerate Voltage

• Magnetic field• Conductor• Relative motion

Electromagnetic Induction

RELATIVE MOTION

MAGNET

COIL (CONDUCTOR)

VOLTMETER

INDUCED CURRENT

INDUCED CURRENT

• Faraday discovered that a changing magnetic flux leads to avoltage in a wire loop– Induced voltage (emf) causes a current to flow !!

Symmetry: electricity magnetism

– electric current magnetic field

– magnetic field electric current

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Experimental Observation of Induction•The next part of the story is that a changing magnetic field producesan electric current in a loop surrounding the field

–called electromagnetic induction, or Faraday’s Law

Bar magnet moves through coil Current induced in coil vS N

Reverse pole Induced current changes sign vN S

Coil moves past fixed bar magnet Current induced in coil

S N

Bar magnet stationary inside coil No current induced in coil

N S

Direction of Induced Current

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• Consider the B field lines that passthrough a surface– define magnetic flux B

– is angle between B and the normalto the plane

– Flux units are T-m2 = webers

Magnetic Flux

B A cos

• How to change the flux?– Changing B or A or will change the flux.

Direction of Induced emf

B

MOTION OFCONDUCTOR

INDUCEDCURRENT

N S

“LEFT HANDGENERATOR RULE”(electron flow)

= 0 = 0.707 B A = B A

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Faraday’s Law of Induction : Magnetic flux through awire loop changing in time produces an EMF in a wire loop:

tN B

induced

emf

numberof loops

rate of changeof flux with time

The faster the change, the larger the induced emf The induced emf is a voltage Minus sign from Lenz’s Law: Induced current produces a magnetic

field which opposes the original change in flux :Jika dlm kumparan flux bertambah, arus yang timbul krn adanya ggl induksitsb akan menghasilkan suatu flux yang “mencoba” meniadakan penambahanflux dalam kumparan tadi.

Motional Emf

• Consider a conducting rod moving on metal rails in a uniformmagnetic field:

( ) ( ) Bd d BA d BLx dxBLdt dt dt dt

BLv

Current will flow counter-clockwise in this “circuit”

• We have treated this situation by using Faraday’s Law for theclosed loop shown in the figure.

• Flux through the loop changes because the area changes.• There is still an induced emf in the moving rod even without

the presence of the metal rails– This is why it is called motional emf

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• Consider two neighboring coils:– if current changes in coil #1, an emf is induced in coil #2

– B– B I1– rewrite as:

Mutual Inductance (induktansi bersama)

12

dNdt

12 dIM

dt

M is the “mutual inductance”units = Henry (H)

Self-inductance

(a) A current in the coil produces a magnetic field directedto the left.

(b) If the current increases, the coil acts as a source of emfdirected as shown by the dashed battery.

(c) The induced emf in the coil changes its polarity if thecurrent decreases.

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Self Inductance

• A coil of wire with achanging current canproduce an EMF withinitself.

• This EMF will opposewhatever is causing thechanging current

• So a coil of wire takes on aspecial name called theinductor (L)

d dIN Ldt dt L is the self-inductance

(induktansi diri)units = “Henry (H)”

InductorsInductorsInductor are used in electrical circuitsbecause they store energy in theirmagnetic fields.

What is an Inductor?

A coil of wire that cancarry current

Energy is stored in the inductor

Current produces a magnetic field

Flux

iCurrent

Definition of voltage: ddtv =

didtv = L

+v–

i

The stored energy in inductor:

= ½ LI2 Joule

L = Henries (physical property of inductor)

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From the Construction

• Inductance

ANL2

N = number of turns on the coil

= permeability of the core (henrys/m)

A = cross sectional area (m2)

l = length of core (m)

L = inductance in henrysMaterial of permeability 0 = 4 10–7 henries/meter can vary between 0 and 10,0000

Transformers• A device that transfers energy by

electromagnetic induction• Used to raise voltage (“step-up

transformer”) or lower voltage (“step-down transformer”)

• Voltage is raised when the primarywinding has fewer turns than thesecondary winding, and voltage islowered when the primary winding hasmore turns than the secondary winding

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TransformersPurpose: to change alternating (AC) voltage to a bigger (or

smaller) value

tNV Bpp

tNV Bss

p

pB

NV

t

input AC voltagein the primaryproduces a flux

changing fluxin secondaryinduces emf

p

sps NNVV

sspp VIVI

s

p

s

p

p

s

NN

VV

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Transformers: Sample Problem 1• A transformer has 330 primary turns and 1240

secondary turns. The input voltage is 120 V andthe output current is 15.0 A. What is the outputvoltage and input current?

p

sps NNVV

VV 451330

1240120 step-up

transformer

sspp VIVI p

ssp VVII A

VVA 456

12045115 .

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Transformers: Sample Problem 2If 120 V of ac are put across a 50-turn primary, what will be the voltage andcurrent output if the secondary has 200 turns, and is connected to a lamp ofresistance 80 ?

(120 V)/50 = (?V)/(200), so ? = 480 VCurrent = voltage/resistance = 480/80 = 6 A

What is the power in the secondary coil?

Power = voltage x current = 480 V x 6A = 2880 W

Can you determine the current drawn by the primary coil? If so, what is it?

Current = power/voltage, and power input = power out = 2880Wso, current = 2880/120 = 24 A

p

sps NNVV

More Applications of Magnetic Induction• Tape / Hard Drive / ZIP Readout

– Tiny coil responds to change in flux as the magneticdomains (encoding 0’s or 1’s) go by.

• Credit Card Reader– Must swipe card generates changing flux– Faster swipe bigger signal

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Microphone

Tape recorder

“Dynamic” Microphones(E.g., some telephones)Sound oscillating pressure waves oscillating [diaphragm +

coil] oscillating magnetic flux oscillating induced emf oscillating current in wire

More Applications of Magnetic Induction• Magnetic Levitation (Maglev) Trains

– Induced surface (“eddy”) currents produce field in opposite direction Repels magnet Levitates train

– Maglev trains today can travel up to 310 mph Twice the speed of Amtrak’s fastest conventional train!

– May eventually use superconducting loops to produce B-field No power dissipation in resistance of wires!

NS

rails“eddy” current

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Sample Problem: Induced currents 1• A circular loop in the plane of the paper lies in a 3.0 T magnetic field

pointing into the paper. The loop’s diameter changes from 100 cm to60 cm in 0.5 s– What is the magnitude of the induced emf?– What is the direction of the induced current?– If the coil resistance is 0.05 , what is the induced current?

– Direction = clockwise (Lenz’s law)– Current = 3.016 / 0.05 = 60.3 A

2 20.3 0.53.0 3.016Volts

0.5BdVdt

tN B

Sample Problem: Induced currents 2• A circular loop (kumparan) terdiri dari 50 lilitan mula-mula berada

dalam medan magnet hingga luas permukaannya merangkap fluxsebesar 3.1x10-4 Wb, jika kumparan bergerak dalam waktu 0.02 smaka fluxnya berubah menjadi 0.1 x 10-4 Wb. Tentukan ggl (emf)yang terinduksi dalam kumparan.

V0.75s0.02

Wb10 x0.1)(3.1504

• Batang tembaga panjang 30 cm terletak tegak lurus terhadap medanmagnet yang fluxnya 0.8 Wb/m2. Batang digerakkan dengan laju 0.5 m/stegaklurus medan. Hitung ggl (emf) yang terinduksi di dalam batangtembaga tsb.

BLv = 0.12 V

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Sample Problem: Induced currents 3 A solenoid is made from besi mempunyai

diameter 15 cm dan panjang 50 cm yangdililit 3000 lilitan. Jika nilai permeability besi adalah 7500, a). berapa induktansi dirisolenoid tersebut dan b). Berapa nilai rata2ggl (emf) yang terimbas (terinduksi) didalamsolenoid kalau arus didalamnya dalamwaktu 0.05 s, diturunkan dari 0.8 A menjadi0.1 A?.

A coil of wire has 400 turns and flowed by a constant current of 2A, maka akan menimbulkan flux sebesar 10-4 Wb menembuslilitan kumparan tersebut. Calculate: a). Emf yang timbul dalamcoil jika arus mengalir dalam waktu 0.08 s, b). Induktansi L daricoil, dan c). Energi yang tersimpan dalam coil.

ANL2

didtv = L

Motors Generators

Electrical mechanical energy Mechanical electrical energy

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Electric Generators• Rotate a loop of wire in a uniform magnetic field:

– changing changing flux induced emf–B = B A cos = B A cos(t) Rotation: = t

cos( ) sin( )Bd d tN NBA NBA tdt dt

This is how electricity isgenerated

Water or steam (mechanicalpower) turns the blades of aturbine which rotates a loop

Mechanical power convertedto electrical power

Current is supplied from an externalsource of emf (battery or power supply)

Forces act to rotate the wire loop

A motor is essentially a generatoroperated in reverse!

Electric Motors

Forces act to rotate the loop towards thevertical.

Once the loop is vertical, the current switchessign and the forces reverse, in order to keep theloop inrotation.

This is why alternating current is necessary fora motor to operate.

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JAPAN 's SHINKANZEN

CHINA 's CRH2

FRANCE ' TGV

SPAIN 's AVE

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INDIAN 's ALL ABOARD

AndPakistan !!!!!

Materi Fisika Listrik 7 Induksi Magnet

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