Rate of Field Change for Induced Current of Loop

  1. Feb 21, 2012 #1
    1. The problem statement, all variables and given/known data

    A single conducting loop of wire has an area of 8.0×10−2 m^2 and a resistance of 110 Ω. Perpendicular to the plane of the loop is a magnetic field of strength 0.37 T.

    At what rate (in T/s) must this field change if the induced current in the loop is to be 0.33 A?

    2. Relevant equations

    Trying to solve for ΔB/Δt

    3. The attempt at a solution

    We have a change in magnetic flux, but it seems to be due to ΔB rather than ΔA, so Δflux = ΔB*Acosθ (However since cos(90) = 0, I'm not sure if this will be correct).

    Using Faraday's Law |ε| = N|(Δflux/Δt)|
    Substituted Δflux = ΔB*A into Faraday's Law --> ε = N(ΔB*A/Δt)
    Substituted the equation for the induced EMF into I = |ε|/R and solved for ΔB/Δt
    ΔB/Δt = I*R/A (N=1 because the loop has 1 turn)

    453.75 T/s = (.33A)*(110Ω)/(8.0*10^-2 m^2)
    asks for 2 significant digits -> 450 T/s = Final Answer

    I'm not sure where I'm going wrong...
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 21, 2012 #2
    θ would not be 90 as Area vector and B make 0 angle
     
  4. Feb 21, 2012 #3
    Okay, then cos(0) = 1, which would prove that my assumption Δflux = ΔB*A*cos(0) = Δflux = ΔB*A

    How does the rest of my thought process look?
     
  5. Feb 21, 2012 #4
    as as i know you are doing correctly ,
    where are you stuck ?
     
  6. Feb 21, 2012 #5
    Mastering Physics tells me this is the wrong answer, though it does not give any explanation as to why.
     
  7. Feb 21, 2012 #6
    what is " mastering physics "
     
  8. Feb 21, 2012 #7
    It's the online website for our physics homework. When you enter your answer, you are told whether or not your answer is correct. You are given 5 attempts, during which the points you earn diminish.
     
  9. Feb 21, 2012 #8
    Even I am in confusion as they have given magnitude of magnetic field
    (which means a constant field ) but asking find at what rate it would vary
     
  10. Feb 21, 2012 #9
    Yes, I noticed this as well. I purposely left that out of my equation as we are attempting to solve for ΔB/Δt. I assume it's the authors of the homework trying to trick us into thinking the value is necessary. Though I cannot see how it could be.
     
  11. Feb 21, 2012 #10
    I am sorry as I fail to help you further with this problem
     
  12. Feb 21, 2012 #11
    You know the resistance of the loop and you know the current so you should be able to find the induced emf
     
  13. Feb 21, 2012 #12
    "I am sorry as I fail to help you further with this problem "

    Thanks, Kushan. I appreciate your help. I think there might be an issue with the website. It wouldn't be the first time.

    Technician: You might notice that is exactly what I attempted to do... No worries though.
     
  14. Feb 21, 2012 #13
    As it turns out, the website wanted a different number of significant figures. Albeit, an incorrect number with the given information...
     
  15. Feb 22, 2012 #14
    Thank god
     
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