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Calcuating the integral E.ds for the paths given, what did i do wrong?

  1. Nov 26, 2005 #1
    Hello everyone i'm stuck on this:
    3. [HRW7 30.P.034.] Figure 30-56 shows two circular regions R1 and R2 with radii r1 = 14.0 cm and r2 = 35.0 cm. In R1 there is a uniform magnetic field of magnitude B1 = 50.0 mT into the page and in R2 there is a uniform magnetic field B2 = 75.0 mT out of the page (ignore fringing). Both fields are decreasing at the rate of 8.10 mT/s.
    Calculate the integral E.ds for each of the three dashed paths.

    (a) path 1 wrong check mark V
    (b) path 2 V
    (c) path 3 wrong check mark V

    I did the following:
    Flux b1 = BA = (.05)(PI)(.14) = .02199;
    Then i was confused on what I was supppose to do with the given information that the fields are decreasing at a rate of 8.10 mT/s, i saw an example in the book and they divided by that amount so i tried that and got:
    2.71495 V which was wrong for path 1. I also tried -2.71495 V which was also wrong. What am i not doing right? Thanks.
  2. jcsd
  3. Nov 26, 2005 #2


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    Finding the flux is not enough. You have to be finding the CHANGE in flux. This can be due to two things. A change in the area A or the change in the magnetic field intensity B. Are you expected to know calculus?
  4. Nov 27, 2005 #3


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    This is a constant rate (rather, it is an instantaneous rate of flux change).
    No calculus is needed.
    But you DO need your thumb in the direction of the negative change of B (flux). The actual B-field doesn't matter in this regard, only its CHANGE.
  5. Nov 28, 2005 #4
    When you say change of the b-field...LIke for the dashed path for loop 1, do i find the Magnetic field of that, then of loop 2, then subtract those two to get the change in magnetic flux? Or do i have to also think of that big outter loop as doing somthing? Because I see Loop 1 and Loop 2 are in different directions so those must subtract. But the big loop and the smaller loop 1 are in the same directinos, so do i add up those 2 loops?(big loop and loop 1). THen do I subtract Loop 2 since its in the opposite direction?
  6. Nov 28, 2005 #5
    I tried finding FLux B1 = B*A = 50.0E-3*PI*.14^2 = .0030788;
    B2 = 75.0E-3*PI*.35^2 = .028863, subtracted B2-B1 = .025784 which was wrong
  7. Nov 29, 2005 #6


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    When I meant change in magnetic field, I meant change in the magnetic field, not anything to do with the dashed loops, because they are dashed loops. In this question, the change in magnetic field (and thus change in flux) has been given to you. The voltage induced in any closed loop is proportional to the change in flux enclosed by the loop.
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