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Homework Help: Maximize the magnetic field in a solenoid

  1. Mar 31, 2010 #1
    1. The problem statement, all variables and given/known data
    Assuming we have equal volumes in both scenarios, which would maximize the magnetic field in a solenoid: a thick and short wire or a thin and long wire.

    2. Relevant equations
    m= the number of layers of wire

    3. The attempt at a solution

    The answer is clearly a thin and long wire because of the equation B=unI, but I was suppose to use the equation I listed under "relevant equations". According to that equation, if we use a thicker wire, the number of layers of wire would increase but the radius would increase. So based on that equation, how am I suppose to realize that a long and thin wire maximizes the field?
  2. jcsd
  3. Apr 1, 2010 #2
    Re: Solenoid

    The equation listed looks like the one for a (flat) circular coil.
    The one used is for a long solenoid.
    The field in the centre of such a solenoid is given by
    B= μonI
    where n is the number of turns of wire per unit length.
    Your reasoning is correct if the question refers to a solenoid.
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