PhysicsLAB Resource Lesson
Motional EMF

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As stated in our previous introductory lesson on induced emf, Faraday's Law of Induction states
ε = -N(ΔΦ/Δt)
  • ε is the induced voltage in a coil, measured in volts
  • N is the number of loops in the coil
  • Φ is the number of flux lines, Φ = BperpendicularA
  • ΔΦ is the changing flux, measured in webers
  • Δt is the time over which the change occurs, measured in seconds
When the number of flux lines is constant, no emf is induced in a coil. The number of flux lines can be changed in two ways:
  • by changing the strength of the magnetic field OR
  • by changing the area of the coil.
In this lesson we will investigate the second case when an emf is induced by changing a loop's cross-sectional area that is exposed to a constant external magnetic field. This is called motional emf.

The following physlets show two ways of changing the coil's area and the resulting induced emf:
Sample Problem
In the following diagram, suppose that the green cross bar is moving to the right at a constant velocity, v. As it moves, the area of the "loop" presented to the magnetic field (+z) increases consequently allowing more flux lines to pass through the "loop" and generating an emf in the "loop."
ε = -N(ΔΦ/Δt)
ε = -N (BperpendicularΔA) /Δt
ε = -NBperpendicular (Δw) /Δt
ε = -NB perpendicular (Δw/Δt)
ε = -NB perpendicular v
and obeys the formula
motional ε = - NBperpendicularv
The right-hand curl rule is used to determine the direction of the induced emf/current. In this formula, v is the constant velocity in m/sec with which the loop is moving into or out of the magnetic field and is the length of the side of the loop which does not change.
 As the bar moves to the right, will a clockwise or counterclockwise current be induced in the left side of the coil?

Calculate the amount of force required to keep the bar moving at a constant velocity.

 As the bar moves to the right, calculate the amount of electrical power dissipated through the resistor.

We will now look at these two AP essays to verify that you understand the principles of induced emf.

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Catharine H. Colwell
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