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Induced voltage

  1. Jun 15, 2012 #1
    1. The problem statement, all variables and given/known data
    A conductor 1 cm in length is parallel to z axis and rotates in a radius of 25 cm at 1200 rev/min , find induced voltage if radial field is given by B = 0.5 a[itex]_{r}[/itex]

    2. Relevant equations



    3. The attempt at a solution
    i am confused. If there is no closed path then how the voltage can be induced
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jun 16, 2012 #2

    rude man

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    Voltage (actually emf) is induced in any material of any kind - even a vacuum! - over a length dL:

    dV = (B x dL) * v
    where B is magnetic field and v is the velocity of the element of length dL. Vectors in bold.

    The direction of dL is in the direction of conventional current under the assumption of a closed circuit. But there need not be a closed circuit.
     
  4. Jun 16, 2012 #3

    tiny-tim

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    hi erece! :smile:
    the magnetic field causes a force, so that the electrons to "want" to move along the wire

    whether they can is irrelevant … there is a gravitational potential difference between the table and the floor even if the things on the table cannot fall to the floor! :biggrin:

    voltage = potential energy difference per charge = work done per charge (V = W/q)

    work done = force "dot" displacement

    for example, if a rod of length L moves at speed v perpendicularly to a uniform magnetic field B, then the force on a charge q inside the rod is qvB along the rod,

    so the work done moving it a distance L along the rod is ∫ qvB dx = qvBL,

    and the work done per charge is vBL,

    ie V = vBL​

    ok, that's for linear motion, where v is constant (along the rod) …

    in your case, v changes along the rod, so the work done integral (∫ qvB dx) will be more complicated :smile:
     
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