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Transcript of CHAPTER 21 ELECTROMAGNETIC INDUCTION - 21.pdf  1 CHAPTER 21 ELECTROMAGNETIC INDUCTION BASIC...

  • 1

    CHAPTER 21

    ELECTROMAGNETIC

    INDUCTION

    BASIC CONCEPTS

    Faradays Law

    Lenzs Law

    Motional emf

  • 2

    Electric Charge Produces an

    Electric Field

    Moving Electric Charge Produces a

    Magnetic Field

    Now Changing Magnetic Field Produces an

    mf

  • 3

    a potential difference (voltage)

    What is changing and causing

    the emf is the magnetic flux.

  • 4

    We defined Electric Flux

    =

    Magnetic Flux is similar

    =

    Flux through an area

  • 5

    We will define a vector to

    represent area. The direction

    of the vector will be

    perpendicular to the surface.

    The length of the vector will be

    the area of the surface. The

    vector will be .

    The flux will be

  • 6

    First, flat area perpendicular to

    = 0 =

  • 7

    For a surface parallel to

    = 90 = 0

    And for in between

    =

    =

  • 8

    If this flux changes an emf will

    be induced in the area.

    Consider a copper coil with one

    loop

    B A

    r

  • 9

    =

    For N loops

    =

    B A

    r

    N loops

  • 10

    FARADAYS LAW

    The emf induced in a circuit is

    directly proportional to the

    time rate of change of the

    magnetic flux through the

    circuit.

    Or

    =

  • 11

    If changes with time an emf, , will be produced.

    Coil in magnetic field.

  • 12

    Flux through coil

    =

    Flux can change:

    1. Magnitude of changes.

    2. Area of loop changes.

  • 13

    3. The angle changes.

    4. Any combination of the

    three.

  • 14

    Example:

    Consider a coil with 200 turns

    on a rectangular frame, 20 cm

    by 30 cm. The resistance of the

    coil is 2 .

  • 15

    If increases uniformly from zero to 0.5"#/% in 0.8 s what is the current in the coil?

    = &0.2%(&0.3%( = 0.060%

    At = 0 = 0

    At = 0.8 = =&0.5"#/%(0.060% = 0.03"#

  • 16

    || = & = 0( & = 0.8(0.8

    || = 200&0.03"#(0.8

    || = 7.5/

    The current will be

    0 = 1 =7.5/2 = 3.75

  • 17

    Lenzs Law

    A changing magnetic flux will

    cause an emf and if the emf is

    in a conductor there will be a

    current.

    What will be the direction of

    the current?

    Lenzs Law will answer that

    question.

  • 18

    The polarity of the induced emf

    is such that it tends to produce

    a current that will create a

    magnetic flux to oppose the

    change in magnetic flux

    through the loop.

  • 19

    a. Magnet moves toward loop.

    Magnet field is down and

    increasing. Induced emf and

    thus current will be ccw to

    oppose the increase.

  • 20

    b. Magnet moves away from

    loop. Magnetic field is up and

    but decreasing.

    Induced current gives magnetic

    field to oppose the decrease.

  • 21

    Motional emf

    x

  • 22

    In time t the rod will move x.

    The area covered in t will be

    = 34

    4 = 5

    = 35

    Faradays Law

  • 23

    =

    = = 35

    = 35 = 35

    A conducting rod moving in a

    magnetic field will have an emf

    Induced across it given by this

    equation.

  • 24

    Example: My airplane

    Luscombe 8E

    Built 1947

    Wingspan 22 feet = 6.7m

    Speed 100 mph = 44.7 m/s

  • 25

    If I am flying it at a point on

    earth where the vertical

    magnetic field is 5410789 what is the voltage drop across the

    wings?

    = :5

    = &5410789(&6.7%(&44.7%/(

    = 1.54107/

  • 26

    Consider a loop around a long solenoid.

  • 27

    The current in the solenoid is increasing

    so the flux through the loop is

    increasing.

    An emf is induced in the loop by

    .

  • 28

    INDUCTANCE

    BASIC CONCEPTS

    Mutual Inductance

    Self Inductance

    Magnetic Field Energy

    Circuits with Inductors

  • 29

    Mutual Inductance

    I1 #1

    = >

    If I1 changes with time t

    0>

    ?@ABCCCD > E=

  • 30

    Put second coil at P

    I1 #1 #2

    F

    ?@ABCCCDGHG:#2

  • 31

    ?@ABCCCD 0

    If I1 changes with time

    For example 0> = 0JGHK

    Then > = JGHK

    And

    = LM

  • 32

    Or = JKK

    And

    0 = 1 =JK

    1 K

    I1 #1 #2

    I2

  • 33

    N = >0> =PJ >: 0>

    0>

    N = PJ >: =PJ>

    :

    Only depends on geometry, number of

    turns, area and length.

  • 34

    Self Inductance

    If the current is changing then there will be

    a changing magnetic flux through the coil.

  • 35

    A changing magnetic flux will induce an

    emf.

    = @L@

    Therefore we define in analogy to the

    mutual inductance

    3 = G

    This is Self-Inductance

    Solve for

  • 36

    = 3G

    Faradays Law

    = QLRQ = 3QQ

    Self-Induced emf

    = 3 G

  • 37

    What is the inductance, 3, of the black coil?

    3 = S0

    TUU@ = PJ >: 0>

    = PJ >: 0>

    3 = >PJ>: 0>

    0> = PJ

    >:

    Area

    A

  • 38

    Magnetic Field Energy

    Consider the coil

    [Type a quote from the document or the summary of an interesting point. You can position the text box

    anywhere in the document. Use the Drawing Tools tab to change the formatting of the pull quote text

    box.]

    Current starts at zero and increases to 0.

  • 39

    =VW = 01 = /

    1 = 0/ Or

    = = 0 And

    = 3 0

    |=| = 0 X3 0Y = 030

    Power is work per unit time.

    = = "

  • 40

    " = = = 03 0 = 300 How much work to bring current through

    inductor from zero to 0?

    To calculate the work integrate from zero

    current to current I

    We wont do it but you may see how on the

    next page.

  • 41

    " = Z 30[0 = 3 Z 0[0

    \

    J

    \]\

    \]J

    " = 12 30

    "^ _UA UBCCCD `W[ HWab

  • 42

    The energy stored in the magnetic field is

    c = 12 30

    Apply to solenoid

  • 43

    /:d%W = :

    = PJ >: 0 So

    0 = :PJ>

    3 = PJ >

    :

    Put into equation for c

    c = 12 30 = 12 PJ

    >

    : X

    :PJ> Y

  • 44

    c = 12

    :

    PJ

    c = 12PJ &:(

    And

    /:d%W = : So

    HWab/:d%W =

    12

    PJ &:(&:(

    d = 12PJ

    Energy stored in magnetic field of coil.

  • 45

    R-L Circuit

    Consider this circuit

  • 46

    First consider that switch > is closed and calculate how the current will increase with

    time.

    Second, then while there is a current in the

    circuit consider opening > and closing ` and calculate how the current will decay.

    Close >

  • 47

    At time = 0 close switch. Kirchkoffs loop starting at the switch and

    going ccw.

  • 48

    G1 3 G = 0

    G =

    G13

    G =

    3

    13 G

    At t = 0 i=0

    Then

    X0Y]J = 3

    After long time

    0 = 0

  • 49

    And

    0 = 1

  • 50

  • 51

    The L-C Circuit

    The capacitor has been charged to an initial

    charge e and then placed across the inductor.

  • 52

    The L-C Circuit

    Remember energy in

    Capacitor cf = >ghi

    And

    Inductor c = > 3G

    Then study

  • 53

  • 54

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