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Magnetic field inside a Solenoid

  1. Dec 11, 2014 #1
    1. The problem statement, all variables and given/known data
    Can I derive an equation for magnetic field inside a solenoid using the formula for magnetic field on the axis of a current carrying coil?

    2. Relevant equations
    B = μI/2r ( Magnetic field at the centre of a current carrying coil)


    3. The attempt at a solution
    B = μI/2r
    Let the number of turns per unit length of the solenoid be 'n' and its length be 'a'
    So,
    B = μnaI/2r
    Which is definitely not equal to μnI (Calculated using Ampere's Circuital Law)
    What's wrong?
     
  2. jcsd
  3. Dec 11, 2014 #2

    ehild

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    The formula refers to the magnetic field of an infinitely long straight current-carrying wire, at distance r from the wire. It is not valid in the centre of a loop.
     
  4. Dec 12, 2014 #3

    rude man

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    Plus, the formula for the mag field around an infinite, current-carrying wire is B = μI/2πr, not what you wrote.
     
  5. Dec 12, 2014 #4
    Well, my teacher has been using that formula...

    loopa.gif
    The application of the Biot Savart Law on the centerline of a current loop involves integrating the z-component.

    loopa2.gif
    The symmetry is such that all the terms in this element are constant except the distance element dL , which when integrated just gives the circumference of the circle. The magnetic field is then

    loopa3.gif
    So, if we apply the same,
    z = 0 (At the centre of the loop)
    So, B = μI/2R
    Isn't it correct??
     
  6. Dec 12, 2014 #5

    ehild

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    It is correct for the magnetic field at the centre of a single loop. If you have a coil, all loops have their magnetic field inside the other loops. You should use the formula for B(z) and sum (integrate) the contributions of all loops.
     
  7. Dec 12, 2014 #6

    rude man

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    Yes, but tha's for a single loop, using Biot-Savart. Not the thing for here..

    Rather than integrate per post #5 my hint is to form a closed loop going thru the entire solenoid middle and closing outside the solenoid. You can now apply Ampere's law to get B.
    Hint: contributions to the integral outside the loop may be ignored.
     
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