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Calculate the magnetic flux density

  1. Oct 21, 2016 #1
    1. The problem statement, all variables and given/known data
    The magnetic flux density in the vicinity of a large air-cored electromagnet is determined by measuring the induced flow of charge in a small coil as the current in the electromagnet is switched on -- see the diagram below.

    cf68e9f8a617.jpg

    Calculate the magnetic flux density at the position of the small coil, due to the electromagnet from the following data: radius of small coil = 10 mm, resistance per unit length of wire of small coil = 0.10 Ω m-1, total flow of charge through the small coil due to switching on the electromagnet = 0.01 C.

    Answer: 0.2 T.

    2. The attempt at a solution
    Q = B A N / R → B = Q R / A N.

    Q = 0.01, R = 0.1 Ω, A = ?, N = 1 turn (assumed).

    A = π r2 = π * (10 / 10 / 100)2 = 3.14 * 10-4 m2.

    B = 0.01 * 0.1 / 3.14 * 10-4 * 1 = 3.18 T.

    What's wrong?
     
  2. jcsd
  3. Oct 21, 2016 #2

    TSny

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    Note that R is not given. Only the resistance per unit length is given.

    Don't assume N = 1.
     
  4. Oct 22, 2016 #3
    Yes, I was also unsure on these things.

    Regarding R: resistance per unit length of wire, while we only have radius. How can we find length?

    Regarding N: how can we find the number of turns on a coil?
     
  5. Oct 22, 2016 #4

    TSny

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    You don't know the value of N. You will just have to include N in your expressions without knowing its value. Cross fingers that it cancels out in the end.
    Can you express R in terms of N and r and the resistance per unit length?
     
  6. Oct 22, 2016 #5
    No idea how to do it. Can't find any formula which includes resistance radius and turns.
     
  7. Oct 22, 2016 #6

    TSny

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    If you knew the total length of wire in the coil, how would you calculate the total resistance of the coil?
     
  8. Oct 22, 2016 #7
    I can only think of R = ρ L / A, but we don't know resistivity ρ, and that's complicating even more.
     
  9. Oct 22, 2016 #8

    TSny

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    The resistance per unit length of the wire is given. Suppose we let the symbol u stand for the resistance per unit length. So, you are given that u = 0.01 Ω m-1. How do you interpret this information? For example, what would be the resistance of 3 meters of length of the wire?
     
  10. Oct 22, 2016 #9
    I would say that 0.01 * 3 = 0.03 Ω. So a wire of 3 m length has a resistance of 0.03 Ω.
     
  11. Oct 22, 2016 #10

    TSny

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    Yes. So, if the total length of wire in the coil is L, how would you express the resistance of the coil in terms of L and u?
     
  12. Oct 22, 2016 #11
    R / L = 0.01 Ω m-1. R = 0.01 L?
     
  13. Oct 22, 2016 #12

    TSny

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    OK. R = Lu. Working with symbols without plugging in numbers is a good idea for this problem. So, try to work out an expression for B in terms of N, r, u, and Q.

    Can you express the total length of wire, L, in terms of r and N? How much is the length of one turn?
     
  14. Oct 22, 2016 #13
    Q = B A N / R → B = Q R / A N

    A is π r2.

    B = Q R / π r2 N.

    R = L u so B = Q L u / π r2 N.
     
  15. Oct 22, 2016 #14

    TSny

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    Very good. Can you express L in terms of N and r?
     
  16. Oct 22, 2016 #15
    Can't find anything on it. No magnetic field formula fits this. Maybe something like L = π (2 * r) N?
     
  17. Oct 22, 2016 #16

    TSny

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    OK. To understand this, note that the coil has N turns. Each turn can be thought of as a circle of radius r. So, what is the length of one turn in terms of r? Then, what is the length of N turns?
     
  18. Oct 22, 2016 #17
    So 1 N = 2 r?
     
  19. Oct 22, 2016 #18

    TSny

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    No. Each turn of the coil consists of a length of wire that essentially has the shape of a circle of radius r. How long is a circle of radius r? That is, what is the formula from geometry that gives you the "length of a circle"?
     
  20. Oct 22, 2016 #19
    Like this?
     
  21. Oct 22, 2016 #20

    TSny

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    The length of a circle is also called the "circumference" of the circle.
     
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