Ch. 28Ch. 28Electromagnetic InductionElectromagnetic Induction

Chapter OverviewChapter Overview

Motional EMFMotional EMF Faraday’s LawFaraday’s Law Lenz’s LawLenz’s Law Magnetic FluxMagnetic Flux Electric GeneratorElectric Generator TransformersTransformers

Motional EMFMotional EMF

If a conductor moves perpendicular to a If a conductor moves perpendicular to a magnetic field, a potential difference is magnetic field, a potential difference is induced across the conductorinduced across the conductor

Moving the conductor in the B-field Moving the conductor in the B-field produces magnetic force produces magnetic force

Charge separation from magnetic force Charge separation from magnetic force produces electric forceproduces electric force

At equilibrium electric force balances At equilibrium electric force balances magnetic force magnetic force

Motional EMFMotional EMF

qvB = qEqvB = qE

Multiply both sides by Multiply both sides by LL

vBL = qELvBL = qEL

ΔΔV = vBLV = vBL

A bar of length 10 cm closes a circuit as shown. The A bar of length 10 cm closes a circuit as shown. The bar moves at 2.0 m/s perpendicular to a B-field of bar moves at 2.0 m/s perpendicular to a B-field of strength .25 T. a) Find the current in the circuit if the strength .25 T. a) Find the current in the circuit if the light bulb has a resistance of 5.0 light bulb has a resistance of 5.0 ΩΩ. b) Ignoring the . b) Ignoring the resistance of the connecting wires find the potential resistance of the connecting wires find the potential difference across the light bulb. Label the higher and difference across the light bulb. Label the higher and lower potential side of the light bulb.lower potential side of the light bulb.

Faraday’s LawFaraday’s Law

In 1820 Oersted demonstrated that a In 1820 Oersted demonstrated that a current could create a magnetic field – i.e. current could create a magnetic field – i.e. that an E-field could produce a B-fieldthat an E-field could produce a B-field

Almost immediately Faraday asked the Almost immediately Faraday asked the opposite question – Could a B-field opposite question – Could a B-field produce an E-field?produce an E-field?

Faraday’s LawFaraday’s Law

Faraday worked on the question for 11 Faraday worked on the question for 11 years until he accidentally found his years until he accidentally found his answer while disconnecting an answer while disconnecting an unsuccessful experimentunsuccessful experiment

Faraday had been searching for a current Faraday had been searching for a current produced by a steady field, but it was a produced by a steady field, but it was a changing field that produced the current changing field that produced the current and he produced the changing magnetic and he produced the changing magnetic field as he disconnected his experimentfield as he disconnected his experiment

Magnetic FluxMagnetic Flux

Magnetic flux Magnetic flux through a single through a single surfacesurface

ΦΦBB = BA cos = BA cosφφ

If a coil has N If a coil has N turnsturns

ΦΦBB = NBA cos = NBA cosφφ

Faraday’s LawFaraday’s Law

An EMF (potential difference) is An EMF (potential difference) is induced when the magnetic flux induced when the magnetic flux through a surface changes in timethrough a surface changes in time

dt

dV

Which of the following can produce Which of the following can produce a changing magnetic flux?a changing magnetic flux?

1 2 3 4 5

0% 0% 0%0%0%

1.1. A changing B-fieldA changing B-field

2.2. A changing areaA changing area

3.3. A changing angleA changing angle

4.4. 1,2, and 31,2, and 3

5.5. None of the aboveNone of the above

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Lenz’s LawLenz’s Law

What pole is induced near coil when a N What pole is induced near coil when a N pole of a bar magnet is inserted into a pole of a bar magnet is inserted into a coil? coil? (OBS)(OBS)

What pole is induced if the N pole is What pole is induced if the N pole is removed form a coil? removed form a coil? (OBS)(OBS)

Reverse the magnet. What poles are Reverse the magnet. What poles are observed now? observed now? (OBS)(OBS)

Lenz’s LawLenz’s Law

The induced EMF is produced so as to The induced EMF is produced so as to oppose the change in magnetic flux oppose the change in magnetic flux producing it.producing it.

A conducting coil is placed over an AC A conducting coil is placed over an AC electromagnet. When the magnet is electromagnet. When the magnet is turned on what will the coil do?turned on what will the coil do?

1 2 3 4

0% 0%0%0%

1.1. NothingNothing

2.2. It will attract to the It will attract to the magnet magnet

3.3. It will repel from the It will repel from the magnetmagnet

4.4. Cannot be determined Cannot be determined

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Lenz’s Law TubeLenz’s Law Tube

Two identically sized disks are dropped. Two identically sized disks are dropped. One is dropped inside a tube in which it One is dropped inside a tube in which it fits. Which will hit the ground first?fits. Which will hit the ground first?

A coil is oriented perpendicular to a B-field A coil is oriented perpendicular to a B-field directed into the page. The coil is at rest. directed into the page. The coil is at rest. What is the direction of the induced current?What is the direction of the induced current?

1 2 3 4

0% 0%0%0%

1.1. ClockwiseClockwise

2.2. CounterclockwiseCounterclockwise

3.3. There is no induced There is no induced currentcurrent

4.4. Cannot be Cannot be determineddetermined

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For the situation depicted, what will For the situation depicted, what will be the direction of the induced be the direction of the induced

current?current?

1 2 3 4

0% 0%0%0%

1.1. ClockwiseClockwise

2.2. CounterclockwiseCounterclockwise

3.3. There is no induced There is no induced currentcurrent

4.4. Cannot be Cannot be determineddetermined

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A wire is formed into a loop of radius .050 A wire is formed into a loop of radius .050 m. The coil is oriented perpendicular to a m. The coil is oriented perpendicular to a uniform B-field of strength .075 T. a) uniform B-field of strength .075 T. a) Sketch the situation. b) The ends of the Sketch the situation. b) The ends of the wire are pulled so that the wire collapses in wire are pulled so that the wire collapses in a time of .060 s. Is an EMF induced? a time of .060 s. Is an EMF induced? Explain. c) Find the magnitude of the Explain. c) Find the magnitude of the induced EMF. d) If a 2.0 induced EMF. d) If a 2.0 ΩΩ resistor is resistor is connected across the ends of the wire, how connected across the ends of the wire, how much power is dissipated. Where did the much power is dissipated. Where did the power come from?power come from?

Applications of Faraday’s LawApplications of Faraday’s Law

Pick up coilsPick up coils GeneratorsGenerators TransformersTransformers

Pick up coilsPick up coils

GeneratorsGenerators

In a generator, a coil In a generator, a coil is turned at a constant is turned at a constant angular frequency in angular frequency in a B-fielda B-field

What produces the What produces the changing flux to changing flux to generate the EMF? generate the EMF? (GR)(GR)

GeneratorsGenerators

Flux is produced by changing angleFlux is produced by changing angle θθ = = ωωtt

ΦΦBB = NAB cos = NAB cos ωωtt

ΔΔV = -dV = -dΦΦ/dt = NAB/dt = NABωω sin sin ωωtt What does the output of a generator look What does the output of a generator look

like? like? (GR)(GR)

AC GeneratorsAC Generators

Output of AC Output of AC Generator is sine Generator is sine wavewave

Can we make a DC Can we make a DC Generator? Generator? (BRST)(BRST)

DC GeneratorDC Generator

To create a DC generator To create a DC generator (such as Genecon) use a (such as Genecon) use a split ringsplit ring

Output for a simple DC Output for a simple DC generator is showngenerator is shown

Output can be made Output can be made smoother by more smoother by more sophisticated sophisticated combinations of rings and combinations of rings and magnetsmagnets

a) What must be the magnetic a) What must be the magnetic field strength so that a field strength so that a generator consisting of 1000 generator consisting of 1000 turns of a coil of radius 25 cm turns of a coil of radius 25 cm produces a peak output of 160 produces a peak output of 160 V when turned at a frequency of V when turned at a frequency of 60 Hz? b) Sketch a graph of 60 Hz? b) Sketch a graph of the output of the generator.the output of the generator.

Why AC?Why AC?

In the early days of electrification, there In the early days of electrification, there was a debate of whether power was a debate of whether power companies should supply ac or dccompanies should supply ac or dc

Edison favored dc whereas Westinghouse Edison favored dc whereas Westinghouse favored acfavored ac

Clearly Westinghouse won the debate. Clearly Westinghouse won the debate. Why?Why?

TransformersTransformers

Electromagnetic induction can be used to Electromagnetic induction can be used to change ac electric potential from one change ac electric potential from one value to anothervalue to another

TransformersTransformers

Flux through one coil is the same Flux through one coil is the same everywhereeverywhere

ddΦΦBB/dt is the same for each coil/dt is the same for each coil

VVpp = -N = -Np p ddΦΦBB/dt and/dt and

VVss = -N = -Ns s ddΦΦBB/dt /dt

After a little algebraAfter a little algebra

p

s

p

s

V

V

N

N

TransformersTransformers

If the number of turns in the secondary is If the number of turns in the secondary is greater than in the primary, is the greater than in the primary, is the secondary potential greater or less than secondary potential greater or less than the primary? the primary? (GR)(GR)

If the number of turns in the secondary is If the number of turns in the secondary is less than in the primary, is the secondary less than in the primary, is the secondary potential greater or less than the primary? potential greater or less than the primary? (GR)(GR)

TransformersTransformers

If the number of turns in the secondary is If the number of turns in the secondary is greater than in the primary, the secondary greater than in the primary, the secondary potential is greater. This is called a potential is greater. This is called a step step upup transformer transformer

If the number of turns in the secondary is If the number of turns in the secondary is less than in the primary, the secondary less than in the primary, the secondary potential is less than the primary. This is potential is less than the primary. This is called a called a step downstep down transformer transformer

Ex. To operate a neon sign a Ex. To operate a neon sign a potential difference of 12000 V is potential difference of 12000 V is needed. What must be the ratio needed. What must be the ratio of turns if the primary potential is of turns if the primary potential is 120 V?120 V?

A DC potential of 100 V is applied to the A DC potential of 100 V is applied to the primary of a step-up transformer with primary of a step-up transformer with turns ratio of 500. What is the potential turns ratio of 500. What is the potential difference across the secondary?difference across the secondary?

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1 2 3 4

25% 25%25%25%

1.1. .2 V.2 V

2.2. 50,000 V50,000 V

3.3. 0 V0 V

4.4. Not enough information Not enough information givengiven

120 V ac is applied across the primary of a step 120 V ac is applied across the primary of a step down transformer with turns ratio 1/50. How does down transformer with turns ratio 1/50. How does the power applied at the primary compare to that the power applied at the primary compare to that at the secondary? (Assume a lossless at the secondary? (Assume a lossless transformer)transformer)

1 2 3 4

0% 0%0%0%

1.1. It is 1/50 th as bigIt is 1/50 th as big

2.2. It is 50 x biggerIt is 50 x bigger

3.3. It is the sameIt is the same

4.4. Not enough information Not enough information to answerto answer

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Power and Current in TransformersPower and Current in Transformers

Conservation of Energy implies Conservation of Energy implies power at primary is the same as power at primary is the same as power at secondarypower at secondary

What happens to current?What happens to current?

IIssVVss = I = IppVVpp so so

s

p

p

s

V

V

i

i

Current in TransformersCurrent in Transformers

In a step up transformer, current is In a step up transformer, current is decreaseddecreased

Is step down transformer current is Is step down transformer current is increasedincreased

Application to Power GenerationApplication to Power Generation

Need to minimize losses in transmissionNeed to minimize losses in transmission Losses given by iLosses given by i22R, so lower current means R, so lower current means

less lossless loss Transmitting at higher potential decreases Transmitting at higher potential decreases

currentcurrent

Self InductanceSelf Inductance

If you apply current to a coil, If you apply current to a coil, you will induce an EMFyou will induce an EMF

V = - dV = - dΦΦ/dt = -d(/dt = -d(μμ00niNA)/dt = niNA)/dt =

- - μμ00nINA di/dtnINA di/dt

The induced EMF is The induced EMF is proportional to the change in proportional to the change in current V = -Ldi/dtcurrent V = -Ldi/dt

Where L = Where L = μμ00nn22Al is called Al is called

the inductance of the coilthe inductance of the coil

A

l

A

RL CircuitsRL Circuits

EX. a) Use Kirchhoff’s Voltage Law to find an equation for the current in the circuit. b) Find a solution if I(0) = 0.

Current grows with exponential asymptote to steady value of E0/R.

Time Constant is given by L/R

Ex. An RL circuit w/o a battery Ex. An RL circuit w/o a battery has an initial current Ihas an initial current I00. Sketch . Sketch

the circuit. b) Use KVL to find the circuit. b) Use KVL to find an equation for the current. c) an equation for the current. c) Find I(t).Find I(t).

Magnetic EnergyMagnetic Energy Circuits do not turn on or off Circuits do not turn on or off

instantaneously.instantaneously. Inductance means that circuits turn on and Inductance means that circuits turn on and

off with a time constant L/Roff with a time constant L/R This is due to the fact that energy is stored This is due to the fact that energy is stored

in the inductor. It takes time to initially in the inductor. It takes time to initially store the energy in the inductor when the store the energy in the inductor when the switch is closed, it takes time to remove the switch is closed, it takes time to remove the energy from the inductor when the switch is energy from the inductor when the switch is opened.opened.

Energy in an InductorEnergy in an Inductor

P = IV = I LdI/dtP = IV = I LdI/dt

For a coil I = B/(For a coil I = B/(μμ00N/l) N/l)

and L = and L = μμ00NN22AlAl

So Energy = So Energy = 1/(21/(2μμ00)B)B22LALA

2

2

1LIdt

dt

dILIPdtEnergy