Mobile Conductors

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Mobile Conductors

• Consider conductor moving in a uniform magnetic
  field.
• A charged particle in the rod experiences a
  magnetic force
• The magnetic force causes the free charges in the
  rod to move
• An excess of positive charge is created at one
  end, and the excess of negative charge is created
  at the other end.

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Compensating Electric Field

• Charges concentrating at the ends of the rod
  create a compensating electric field
• Charges stop to move, when the electric and
  magnetic forces compensate each other
• Motion of the conducting rod in a magnetic field
  creates the potential between the ends

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Circuit with Moving Conductor

• Consider the moving rod which slides along a
  stationary U-shaped conductor
• Potential difference Vab causes a current to flow
  in a circuit
• Thus, the magnetic field acting on the moving
  charges creates emf

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Changing Magnetic Flux

• Due to the motion of conductor, the area of the
  loop changes
• The magnetic flux through the loop changes
• Thus

Changing magnetic flux induces the emf and the
current in the loop
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Direction of current

• The current in the loop also creates a magnetic
  field
• Direction of current in the loop is such, that
  the created magnetic field "opposes" to the
  change of the magnetic flux (c.f. Lenz's law)
• Taking into account such direction of the
  current
• Negative sign reflects the fact, that induced emf
  always opposes to the change of magnetic flux.

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Changing Magnetic Flux and emf

• We got for the emf in a loop with changing area
• This relation remains valid if the magnitude of
  the field changes instead of the area of the
  loop
• In general, this result is valid for any loop
  with changing magnetic flux