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Magnetic Field at the centre of Spiral

  1. Oct 9, 2012 #1

    AGNuke

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    A thin insulated wire forms a plane spiral of N = 100 tight turns, carrying a current I = 8 mA. The radii of inside and outside turns are equal to a = 50 mm and b = 100 mm.

    Find the magnetic induction at the centre of the spiral and the magnetic moment of the spiral with the given current.


    This problem I searched all over but nowhere I could found any answer. Hope I'll be helped.

    The figure of planar spiral is given with inner radius and outer radius as mentioned, in case anybody needs a diagram.

    I first calculated the no. of turns per unit width, that would be [tex]n=\frac{N}{(100-50)mm} = 2000\;turns/m[/tex]

    I know the magnetic field due to a current carrying loop with n turns,[tex]B = \frac{\mu _0ni}{2r}[/tex]

    I considered a loop out of spiral of radius r and width dr, thus the total magnetic field would be the summation of all the loops from inner radius to outer radius.[tex]\int \mathrm{d}B=\int_{0.05}^{0.1} \frac{\mu _0ni}{2r}\mathrm{d}r[/tex]

    I tried to calculate but I dodged the answer from a long mile, the answer is [itex]7\; \mu T[/itex]

    Any Help appreciated. And if anybody do not mind, I would also like to get my question asked no too long ago answered too. https://www.physicsforums.com/showthread.php?t=641032
     
    Last edited: Oct 9, 2012
  2. jcsd
  3. Oct 9, 2012 #2

    TSny

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    Watch your unit conversion here. Otherwise, everything looks good.
     
  4. Oct 9, 2012 #3

    AGNuke

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    Its not about unit conversion. I had all done correct. The expression after integration was including ln2, which is not present in the answer.

    Even if I substituted the value of pi or ln2, my answer was really off.
     
  5. Oct 9, 2012 #4

    TSny

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    Your answer for n says that there are only .002 turns of wire in a radial distance of 1 meter. But you know that you have 100 turns in only 50 mm of distance.
     
    Last edited: Oct 9, 2012
  6. Oct 9, 2012 #5

    AGNuke

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    Extremely sorry. Its 2000 turns/m. And the answer I got is 6.4 microTesla.[tex]B=\frac{\mu _0ni}{2}\mathrm{ln}2[/tex]
     
  7. Oct 9, 2012 #6

    TSny

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    Your expression for the answer looks correct. I don't get 6.4 microTesla.
     
  8. Oct 9, 2012 #7

    AGNuke

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    Yeah.... I got something like 6.96. Maybe my calculator was malfunctioning and I didn't bothered to recalculate it on Computer. Fault on my part.

    Can you look at the question I posted long before, unfortunately no one has entertained it as of yet - https://www.physicsforums.com/showthread.php?t=641032
     
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