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Induced tension magnetic field (B)

  1. Mar 6, 2015 #1
    1. The problem statement, all variables and given/known data
    I have the strength of the magnetic field, B, the time, Delta t, a circle formed ring with the diameter, d. I should calculate the induced tension, when the surface is

    (a) parallel to the B field
    (b) 50 degrees on the B field

    Need help to solve it (symbolic if possible).

    2. Relevant equations
    I thought of something like:
    [latex] $U_H = A_H \frac{I B}{d}$ [/latex],
    but I don't have "I". And there are no angles there. Please tell me how to solve it symbolic.

    3. The attempt at a solution
    Please look the (2).
     
  2. jcsd
  3. Mar 6, 2015 #2

    BvU

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    Hello Basip, welcome (back) to PF :smile: !

    Could you please re-read your posting and complete the problem statement ? Perhaps even add a little drawing ? It is now rather unclear what the exercise wants you to do. It's fine if you mention ##\Delta t##, but what it its role in this problem ?

    Also all and any symbols you want to use in part 3 need clarification. ##U_H## is probably the induced emf ? and ##A_H## an area ? Don't let us guess unnecessarily !

    And you can do displayed equations with $## ##$U_H = A_H \frac{I B}{d} $## ##$ to get $$ U_H = A_H \frac{I B}{d} $$ and in-line equations with ##\#\# ##U_H = A_H \frac{I B}{d}##\#\# ## to get things like ##U_H = A_H \frac{I B}{d} ##

    However, your equation doesn't make much sense to me. You sure it fits in the problem context ? Could it be you need something else ?
     
  4. Mar 7, 2015 #3
    Dear BvU!

    Thank you for your help so far. I don't know how to edit my question, so I reply here.

    Variables to play with
    $$B=0.58T$$
    $$ \Delta t=0.10s$$
    $$d=0.105m$$

    Question formulation
    In a magnetic field, B, at the time, ## \Delta t ##, is the surface of a circular conductor loop,d, halved. Calculate the tension, when the surface
    1. is perpendicular to B
    2. has an angular of ##30^\circ## with B
    3. is parallel to B
    How I think it could be solved
    The magnetic flux
    $$\Phi_B = \int_A \vec B d \vec A$$,
    where ##\Phi_B## is the magnetic flux, ##B## is the magnitude of the magnetic field and ##A=\pi r^2## is the areal.

    The induction tension
    $$U_i = \frac{d \Phi_B}{dt} = \frac{\int_A \vec B d \vec A}{dt}$$,
    where ##U_i## is the induction tension.

    1. ##U_i = \frac{\sin(90^\circ) A B}{dt}##
    2. ##U_i = \frac{\sin(30^\circ) A B}{dt}##
    3. ##U_i = \frac{\sin(180^\circ) A B}{dt}##
    Is that correct? Could it be solved this way?

    Questions
    Question 1
    Can I write it this way?
    $$\Phi_B = \int_A \vec B d \vec A.$$
    I think it looks wrong, because we have two integrals on the right side and a number on the left side. How could I write it so it doesn't look wrong? I think there are more than one way to write it correct, so please write more than one solution. I think you could use the cross product sign?

    Question 2
    But now I have solved it the Gaußian way(?). Could I solve it Lorentzian too? I thought of using ##F=q\,\vec v \times \vec B##. The firs formular I suggested is, I think, wrong (it was about the Hall Effect).

    Yours Faitfully,
    and thank you very much in advance!
     
    Last edited: Mar 7, 2015
  5. Mar 7, 2015 #4

    BvU

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    Dear Basip,
    a quick answer I may have to correct when I'm more awake:
    My compliments for your now much clearer post. You have the given variables, the right equation and the right plan to solve. So go ahead !

    As to your questions: 1. yes, it is a bit strange, but correct. Check Faraday's law. That ##\vec {dA}## is a surface area .
    2. I wouldn't consider this the gaussian way. That has to do with divergence. But in both cases a surface integral is needed.
    There is an approach based on the Lorentz force, I think, but I can't investigate now. Check further down in the Faraday link. But it involves more math.
     
    Last edited: Mar 9, 2015
  6. Mar 9, 2015 #5

    BvU

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    Everything has fallen into place ? And all done ? Or are there further questions ?
     
  7. Mar 10, 2015 #6
    Thank you for your help :-)
     
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