Motional emf

  • Motional emf is the voltage induced in a conductor moving through a magnetic field.

Day 133 Xs

  • The magnetic field is into the page (-z) and the velocity is to the right; using the right hand rule, there is an upward force on the proton and a downward force on the electron pushing them to the extreme ends of the conductor as shown.

Production of an Electric Field

  • Since there is a separation of charge in the conductor, an electric field is produced in the conductor.
  • Eventually, for the electron, the magnetic force (down) = the electric force (up) at equilibrium
  • Therefore, qvB = qE; and E=vB
  • Since V=Ed or in this case d=length of the conductor; V=El OR V=vBl OR V=Bl

Derivation of Equation for ε For a Moving Conductor

  • Since V=Ed or in this case d=length of the conductor; V=El OR V=vBL
  • ε = Blv
  • ε = induced emf, in Volts
  • B = magnetic field, in T
  • l = length of conducting bar, in m
  • v = velocity of conductor, in m/s

Potential Difference in the Bar

  • Since the positive charges were forced to the top of the bar, it is at the higher potential
  • Potential difference is maintained across a conductor as long as there is motion through the field.
  • If the motion is reversed, the polarity of the potential difference is also reversed.

A Moving Conductor as Part of a Closed Circuit

  • Use the right hand rule for the current in the conductor to determine the direction of the magnetic force
  • If the bar moves Δx in Δt, then …
  • ΔΦ = BA = Bl(Δx) , if N=1 loop,
  • ε = ΔΦ/Δt = (Bl Δx/Δt) = Blv
  • The induced current, I = ε/R = Blv/R

 

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