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How does one calculate the flux density B at end of solenoid?

  1. Jun 2, 2015 #1
    1. The problem statement, all variables and given/known data
    I came across a recent problem that asked me to calculate the flux density at the end of a solenoid. I was given the current 3 A , the number of turns per unit length , 12 cm-1 and the using the permeability of free space as 4π × 10^-7
    2. Relevant equations
    The equation I used for this is B=μnI , where n is the number of turns per unit length ( in per meter) and I current.

    3. The attempt at a solution
    I got 144π × 10^-5, this however was not an option and so I was wondering if there were some other factor I had to account for as it is the end of the coil and not for the midpoint for which the equation is defined.
     
  2. jcsd
  3. Jun 2, 2015 #2

    NascentOxygen

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    You need to show your working so helpers can first discount that you may have made a simple mistake in the mathematics.
     
  4. Jun 3, 2015 #3
    With all due respect sir, I have no problems using a calculate but ok , never the less:
    You need to convert the 12 per cm to per m which gives you 12/10^-2=1200
    B= 4π×10-7 ×1200 × 3 = 144π×10-5
     
  5. Jun 3, 2015 #4

    gneill

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    Presumably this is a multiple choice style of question?

    Can you quote the problem exactly along with the selection of answers?

    It sometimes happens that a problem is "refreshed" with a slight change in values in order to make it "new" (so last year's answers can't be copied). Occasionally the "refresh" is imperfect: either the new answer is not inserted in the list of answers or the person making the change made an error in calculation...
     
  6. Jun 3, 2015 #5

    NascentOxygen

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    B=µnI gives the flux density midway between the two ends of the solenoid.

    Follow the link in this thread to obtain the formula for B near the end of a solenoid. If I read it correctly, you'll find that right at the end they'll differ by a factor of approx. 2
     
  7. Jun 4, 2015 #6
    The question said "What is the magnetic flux density near the end of a solenoid that has 12 turns per centimeter and carrying a current of 3A? (Assume μo =4π×10-7)
    Answers
    A) 144π×10-7) T
    B) 1.44π×10-7) T
    C) 144π μT
    D) 144π T
     
  8. Jun 4, 2015 #7

    NascentOxygen

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    Looks like correct answer is: (E) none of the above
     
  9. Jun 5, 2015 #8
    Lol yes , a reasonable conclusion
     
  10. Jun 6, 2015 #9
    The two factors are limits for very long and very short solenoid relative to ring radius, so I think that you ask for the assumptions to use on your class level.
     
  11. Jun 6, 2015 #10

    rude man

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    Length of solenoid? 1cm? 1m?
     
  12. Jun 6, 2015 #11

    rude man

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    If length >> radius, answer would be close to A/2.
    If length << radius, B = μ0IR/2
    which is of no help since radius R is not given.
    What you do is sum the B fields due to each wire turn using Biot-Savart. This is most readily done by the appropriate integral, so what you're doing here is assuming a differentially small wire spacing then integrating over distance from the solenoid's end (x=0) to x=infinity, and pre-multiplying by 1/(actual wire spacing).
     
    Last edited: Jun 6, 2015
  13. Jun 6, 2015 #12
    Imagine two exacly identical coils carrying the same current in the same direction. B along the axis of each coil is given by by Nile in post one. Let B at the end points of the coils have the value Be. Now imagine that the two coils are pushed together end to end so as to make a longer coil. B along the axis will have the same value as before. Now consider the midpoint of the axis of this coil, where two ends of the smaller coils meet. B at this point can be considered to be the sum of B at the two ends of the smaller coils and therefore B = 2Be. In other words B at the end points of a long coil is half the value of B within the coil.
     
  14. Jun 6, 2015 #13
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