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Magnetic Field of a Finite Solenoid

  1. May 6, 2014 #1
    The problem statement, all variables and given/known data
    Find the magnetic field generated at the center of a coil of wire with N turns, a radius of r, and a current I running through it



    Relevant equations
    B=μ0nI, where n=N/L (L is the total length of the coil)



    The attempt at a solution
    B=μ0nI
    B=μ0I(N/L)
    L=2πrN
    B=(μ0NI)/(2πrN)
    B=(μ0I)/(2πr)

    However, the correct answer is:
    B=(μ0I)/(2r)

    Why is this? Thank you!
     
    Last edited: May 6, 2014
  2. jcsd
  3. May 6, 2014 #2
    The equation you have given I believe only applies to a "long" solenoid. This is a good approximation as you can see, but it isn't enough. Consider how we would find the magnetic field at the center of ring? Now consider how we would find the find at the center of a collection of rings. Is the answer the same? Should it be the same?
     
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