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-Generators -Motors -Eddy Currents -Maxwell’s Four Equations AP Physics C Mrs. Coyle

-Generators -Motors -Eddy Currents -Maxwell’s Four Equations AP Physics C Mrs. Coyle

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Page 1: -Generators -Motors -Eddy Currents -Maxwell’s Four Equations AP Physics C Mrs. Coyle

-Generators-Motors

-Eddy Currents-Maxwell’s Four

Equations

AP Physics C

Mrs. Coyle

Page 2: -Generators -Motors -Eddy Currents -Maxwell’s Four Equations AP Physics C Mrs. Coyle

Applet Link: http://www.walter-fendt.de/ph14e/generator_e.htm

Electric generators convert mechanical energy to electrical energy

AC Generators• Do not have a

commutator

DC Generators • Have a commutator

Page 3: -Generators -Motors -Eddy Currents -Maxwell’s Four Equations AP Physics C Mrs. Coyle

AC Generator

Page 4: -Generators -Motors -Eddy Currents -Maxwell’s Four Equations AP Physics C Mrs. Coyle

Rotating Loop in a Generator• Loop has N turns

• The flux through the loop at any time t :

B = BA cos

B =BA cos t

sin

Bdε N

dtNABω ωt

Page 5: -Generators -Motors -Eddy Currents -Maxwell’s Four Equations AP Physics C Mrs. Coyle

Induced emf in a Rotating Loop

max = NAB

sin

Bdε N

dtNABω ωt

Page 6: -Generators -Motors -Eddy Currents -Maxwell’s Four Equations AP Physics C Mrs. Coyle

Induced emf in a Rotating Loop

max occurs when t = 90o or 270o

– This occurs when the magnetic field is in the plane of the coil and the time rate of change of flux is a maximum

= 0 when t = 0o or 180o

– This occurs when B is perpendicular to the plane of the coil and the time rate of change of flux is zero

Page 7: -Generators -Motors -Eddy Currents -Maxwell’s Four Equations AP Physics C Mrs. Coyle

DC Generators• The DC (direct current)

generator has essentially the same components as the AC generator

• The main difference is that the contacts to the rotating loop are made using a split ring called a commutator

Page 8: -Generators -Motors -Eddy Currents -Maxwell’s Four Equations AP Physics C Mrs. Coyle

DC Generators

• In this configuration, the output voltage always has the same polarity and pulsates with time

• To obtain a steady DC current, commercial generators use many coils and commutators distributed so the pulses are out of phase

Page 9: -Generators -Motors -Eddy Currents -Maxwell’s Four Equations AP Physics C Mrs. Coyle

Motors

• A motor is a generator operating in reverse

• Electrical energy is converted to mechanical energy

• A current is supplied to the coil by a battery and the torque acting on the current-carrying coil causes it to rotate

Page 10: -Generators -Motors -Eddy Currents -Maxwell’s Four Equations AP Physics C Mrs. Coyle

Back emf of a Motor

• As the coil rotates in a magnetic field, an emf is induced in the coil– This induced emf always acts to reduce the

current in the coil and is called back emf– The back emf increases in magnitude as the

rotational speed of the coil increases

Page 11: -Generators -Motors -Eddy Currents -Maxwell’s Four Equations AP Physics C Mrs. Coyle

• The power requirements for starting a motor and for running it are greater for heavy loads than for light ones

Page 12: -Generators -Motors -Eddy Currents -Maxwell’s Four Equations AP Physics C Mrs. Coyle

Voltage Transformers

Bs s

dV N

dt

Psolenoid o P

NI A

BP P

dV N

dt

SB P

P S

Vd V

dt N N

S PN N step up transformer

P SN N step down transformer

Page 13: -Generators -Motors -Eddy Currents -Maxwell’s Four Equations AP Physics C Mrs. Coyle

Current Transformers

SS P

P

NV V

N

Primary SecondaryP P

P P S SV I V I

P P S SN I N I

PI

SI

Page 14: -Generators -Motors -Eddy Currents -Maxwell’s Four Equations AP Physics C Mrs. Coyle

Eddy Currents • Circulating currents that are

induced in bulk pieces of metal moving through a magnetic field

• The eddy currents are in opposite directions as the plate enters or leaves the field

• Are often undesirable because they represent a transformation of mechanical energy into internal energy

Page 15: -Generators -Motors -Eddy Currents -Maxwell’s Four Equations AP Physics C Mrs. Coyle

Maxwell’s Equations

Gauss's law electric

0 Gauss's law in magnetism

Faraday's law

Ampere-Maxwell lawI

oS

S

B

Eo o o

qd

ε

d

dd

dtd

d μ ε μdt

E A

B A

E s

B s

Page 16: -Generators -Motors -Eddy Currents -Maxwell’s Four Equations AP Physics C Mrs. Coyle

Gauss’s law (electrical):

• The total electric flux, ΦE = , through any closed surface equals the net charge inside that surface divided by o

• This relates an electric field to the charge distribution that creates it

oS

qd

ε E A

E dA

Page 17: -Generators -Motors -Eddy Currents -Maxwell’s Four Equations AP Physics C Mrs. Coyle

Gauss’s law (magnetism):

• The total magnetic flux through any closed surface is zero

• The number of field lines that enter a closed volume must equal the number that leave that volume

• The magnetic field lines cannot begin or end at any point

• Isolated magnetic monopoles have not been observed in nature

0S

d B AdA

Page 18: -Generators -Motors -Eddy Currents -Maxwell’s Four Equations AP Physics C Mrs. Coyle

Faraday’s law of Induction:

• An electric field is created by a changing magnetic flux

• Induced voltage Emf=- around any closed path, equals the rate of change of the magnetic flux through any surface bounded by that path

• Example: A current is induced in a conducting loop placed in a time-varying B

Bdd

dt

E s

dE s

Page 19: -Generators -Motors -Eddy Currents -Maxwell’s Four Equations AP Physics C Mrs. Coyle

Ampere-Maxwell Law

• A generalization of Ampere’s law• Creation of a magnetic field by a changing

electric field and electric currents• The line integral of the magnetic field around

any closed path is the given sum

I Eo o o

dd μ ε μ

dt

B s

Page 20: -Generators -Motors -Eddy Currents -Maxwell’s Four Equations AP Physics C Mrs. Coyle

The Lorentz Force Law

F = qE + qv x B

• Maxwell’s equations, together with this force law, completely describe all classical electromagnetic interactions