Induced EMF in a moving conductor

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Intros
Lessons
  2. Introduction to induced EMF in a moving conductor.
  3. Magnitude of the electromotive force.
  4. Direction of the induced current and electromotive force.
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Examples
Lessons
  1. A 1.2m length of wire is pulled through a uniform 0.045 T magnetic field at 6.7m/s as shown. What emf is generated between the ends of the wire?

    Induced EMF in a Moving Conductor.
    1. 0V
    2. 0.090V
    3. 0.36V
    4. 0.45V
  2. A solid conductor travels at 150m/s across a uniform 0.045T magnetic field. Which side is positively charged and what is the emf across this block?

    Induced EMF in a Moving Conductor.
    1. The circular loop of wire shown below has an area of 0.40 m2m^{2} and is in a 0.60T magnetic field. This filed increased to 1.40 T in 0.25 ss.

      Induced EMF in a Moving Conductor.
      1. A 0.050m long conducting wire is moved through a 1.5 T magnetic field as shown below.

        Induced EMF in a Moving Conductor.


        What is the magnitude of the emf generated between its ends, and in what direction do the electrons in the conductor initially move?

        Induced EMF in a Moving Conductor.
        1. A circular loop of resistance 1.2 Ω \Omega is pulled a distance of 0.40m into a perpendicular magnetic field as shown below.

          Induced EMF in a Moving Conductor.


          an average current of 0.50A is produced in the coil during this event. Calculate the constant speed with which the coil was pulled.
          1. 0.10 m/s
          2. 0.75 m/s
          3. 1.9 m/s
          4. 2.4 m/s
        2. A 0.75 m conducting rod is moved at 8.0m/s across a 0.25 T magnetic field along rails. The electrical resistance of the system is 5.0 Ω \Omega . What are the magnitude and direction through point XX?

          Induced EMF in a Moving Conductor.


          Induced EMF in a Moving Conductor.
          1. A 200-turn coil has a 15.2 V potential difference induced in it when the magnetic field changes from 0.42 T to 0.22 T in the opposite direction in 3.2 ×10?2 ss. What is the radius of this coil?

            Induced EMF in a Moving Conductor.
            1. 3.5 × 10?2m
            2. 5.1 × 10?2m
            3. 5.9 × 10?2m
            4. 6.2 × 10?2m
          Topic Notes
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          In this lesson, we will learn:

          • Moving a conductor in a uniform magnetic field results in an induced emf across the conductor.
          • How to find the magnitude of the electromotive force?
          • How to find the direction of the electromotive force?

          Notes:

          • Moving a conductor in a uniform magnetic field results in an induced emf across the conductor.
          • As the conductor moves, there is a change in magnetic flux, due to the change in area of the conductor that is exposed to the magnetic field lines.

            • Induced EMF in a Moving Conductor.


          • Change in flux results in electromotive force induction and induced emf in the loop.


            • Magnitude of the Electromotive Force


          • According to Faraday’s law:

          ϵ=ΔϕΔt \large \epsilon = \frac{\Delta \phi} {\Delta t}


          ll = length of the rod
          BB = magnetic field
          vv = speed of the rod
          AA = area of the loop

          If the rod moves at speed of vv , it travels a distance of Δx\Delta x , in a time Δt\Delta t ;

          Δx=vΔt \Delta x = v \Delta t

          Therefore, the area of the loop changes by an amount of ΔA\Delta A = lΔxl \Delta x

          ϵ=ϕΔt=BΔAΔt=Blv ΔtΔt=Blv\large \epsilon = \frac{\phi} {\Delta t} = \frac{B \Delta A} {\Delta t} = \frac{Blv \, \Delta t} {\Delta t} = Blv



          Direction of the Induced Current and Electromotive Force

          • The direction of the induced current is in a way to oppose the change in flux.

            • Induced EMF in a Moving Conductor.