Electromagnetic Induction

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					    Electromagnetic Induction
Objective:
 TSW understand and apply the concept of
 magnetic flux in order to explain how
 induced emfs are created and calculate
 their value and polarity.
You will be responsible for the content contained in
chapter 20, sections 1&2 of the textbook. Take the
time to read these sections.


Chapter 20 Homework Problems:
4, 9, 15, 17, 19, 22, 23
Electromagnetic induction is the process
by which an emf (voltage) is produced in a
wire by a changing magnetic flux.

• Magnetic flux is the product of the
  magnetic field and the area through which
  the magnetic field passes.
• Electromagnetic induction is the principle
  behind the electric generator.
• The direction of the induced current due to
  the induced emf is governed by Lenz’s
  Law.
Here is a visual model of what we
        did in chapter 19:


             Loop of wire
                               Output
 Input         and an
                                Force
Current       External
                             (wire moves)
            magnetic field


          Electric Motor
 Here is a visual model of what we
       will do in chapter 20:


              Loop of wire
   Input
                 and an        Output
  Force
                External       Current
(move wire)
              magnetic field


              Generator
 The next two slides contain
vocabulary and equations, you
   should commit them to
           memory
Important Terms
alternating current - electric current that rapidly reverses its direction
electric generator - a device that uses electromagnetic induction to
convert mechanical energy into electrical energy
electromagnetic induction - inducing a voltage in a conductor by
changing the magnetic field around the conductor
induced current - the current produced by electromagnetic induction
induced emf - the voltage produced by electromagnetic induction
Faraday’s law of induction - law which states that a voltage can be
induced in a conductor by changing the magnetic field around the
conductor
Lenz’s law - the induced emf or current in a wire produces a magnetic
flux which opposes the change in flux that produced it by
electromagnetic induction
magnetic flux - the product of the magnetic field and the area through
which the magnetic field lines pass.
motional emf - emf or voltage induced in a wire due to relative motion
between the wire and a magnetic field
     Equations, Symbols, and Units
              where
  BLv       ε = emf (voltage) induced by
                  electromagnetic induction (V)

    
              v = relative speed between a conductor

I
                   and a magnetic field (m/s)
              B = magnetic field (T)
    R         L = length of a conductor in a magnetic

  BAcos
                   field (m)
              I = current (A)
              R = resistance (Ω)
            Φ = magnetic flux (Tm2 = Weber=Wb)
  N        A = area through which the flux is
       t          passing (m2)
               = angle between the direction of the
P  IV             magnetic field and the area through
                   which it passes
                          Magnetic Flux
Consider a rectangular loop of wire of height L and width x
which sits in a region of magnetic field of strength B. The
magnetic field is directed into the page, as shown below:
                                  w



                                         L




The magnetic flux is given by the following equation:

   BAcos                  Φ = The magnetic flux (Tm2 = Wb)
                             B = The magnetic field (T)
                             A = area of loop (m2)
                             Φ = angle between the field and the area
Faraday’s law states that an induced emf is
produced by changing the flux, but how
could the flux be changed?
• Turn the field off or on.
• Move the loop of wire out of the field
• Rotate the loop to change the angle
  between the field and the area of the loop.
Here is Faraday’s Law in equation
form:

                               Where
                             Є = The induced emf (voltage) (V)
 N                           ΔΦ = The change in flux (Wb)
     t                        Δt = The change in time (s)
                               N = number of loops.


 *Note that an emf is only produced if the flux changes. The quicker the
 flux changes the larger the induced emf.
The induced emf in the wire will produce a current in the wire. The
magnitude of the induced current is found using Ohm’s Law:




                            V  IR
                              IR
                                
                             I
                                R
The direction of the induced current is found using Lenz’s Law (conservation of
energy).




 Lenz’s Law – The induced current in a wire produces a
 magnetic field such the flux of the produced magnetic
 field opposes the original change in flux. In simple
 terms the wire resists the change in flux and wants to
 go back to the way things were.
 It is helpful to use RHR#2 when using Lenz’s Law.
Example 1: A circular loop of wire with a resistance of 0.5Ω and
  radius 30cm is placed in an external magnetic field of 0.2T. The
  magnetic field is turned off in .02 seconds.
a) Calculate the original flux of the loop.
b) Calculate the induced emf.
c) Calculate the current induced in the wire.
d) What direction does the induced current have?
e) What other way could the same emf be induced without turning the
   field off?
                        •        •        •     •
                        •        •        •     •
                        •        •        •     •
                        •        •        •     •
                        •        •        •     •
   Let’s do some examples
predicting the induced current
  direction using Lenz’s Law
•       •        •         •   •      •         •         •
•       •        •         •   •      •         •         •
•       •        •         •   •      •         •         •
•       •        •         •   •      •         •         •
•        •        •
    Bout decreasing flux   •   •      •         •
                                   Bout increasing flux
                                                          •
           CCW                             CW


X       X         X        X   X     X         X          X
X       X         X        X   X     X         X          X
X       X         X        X   X     X         X          X
X       X         X        X   X     X         X          X
X       X         X        X   X     X         X          X
     Bin decreasing flux           Bin increasing flux
            CW                           CCW
If you are really struggling applying Lenz’s
Law, then memorize the following table:


                 decreasing   Increasing

       B out        CCW          CW

        B in        CW          CCW
Example 2: A circuit with a total resistance of 5Ω is made using a set
  of metal wires and a copper bar. The magnetic field is directed into
  the page as shown in the diagram. The bar starts on the left and is
  pulled to the right at a constant velocity.
a) Calculate the induced emf in the circuit.
b) Calculate the current induced in the wire.
c) What direction does the induced current have?
d) What is the magnitude and direction of the magnetic force that
   opposes the motion of the bar?
            X       X        X       X          X       X   X
            X       X        X       X          X       X   X
            X       X        X       X          X   v   X   X
                                      L
            X       X        X       X          X       X   X
            X       X        X       X          X       X   X
            X       X        X       X          X       X   X
The last example led to the equation for the motional emf.
The motional emf is the voltage induced in a wire as it
moves in an external magnetic field. The induced emf will
produce a current in the wire, which will in turn result in a
force that opposes the motion of the wire. You don’t get
something for nothing.

Motional emf                 Where
                             Є = The induced emf (V)
                             B = The external magnetic field (T)

       BLv                 L = The length of the wire (m)
                             v = The velocity of the wire (m/s)
Example 3: A conducting rod of length 0.30 m and resistance 10.0 Ω
moves with a speed of 2.0 m/s through a magnetic field of 0.20 T which is
directed out of the page.
                                    v




                                                     L




                        B (out of the
                        page)




  a) Find the emf induced in the rod.
  b) Find the current in the rod and the direction it flows.
  c) Find the power dissipated in the rod.
  d) Find the magnetic force opposing the motion of the rod.
Example 4: A square loop of sides a = 0.4 m, mass m =
    1.5 kg, and resistance 5.0 Ω falls from rest from a
    height h = 1.0 m toward a uniform magnetic field B
                                                             a
    which is directed into the page as shown.
(a) Determine the speed of the loop just before it enters
                                                                 a
    the magnetic field.

As the loop enters the magnetic field, an emf ε and a
     current I is induced in the loop.
(b) Is the direction of the induced current in the loop
                                                                     h
     clockwise or counterclockwise? Briefly explain how
     you arrived at your answer.

When the loop enters the magnetic field, it falls through
  with a constant velocity.                                              B


(c) Calculate the magnetic force necessary to keep the
    loop falling at a constant velocity.
(d) What is the magnitude of the magnetic field B
    necessary to keep the loop falling at a
     constant velocity?
(e) Calculate the induced emf in the loop as it enters and
    exits the magnetic field.

				
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