Rate of Field Change for Induced Current of Loop

  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. Chegg
    θ would not be 90 as Area vector and B make 0 angle
     
  4. 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. as as i know you are doing correctly ,
    where are you stuck ?
     
  6. Mastering Physics tells me this is the wrong answer, though it does not give any explanation as to why.
     
  7. what is " mastering physics "
     
  8. 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. 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. 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. I am sorry as I fail to help you further with this problem
     
  12. You know the resistance of the loop and you know the current so you should be able to find the induced emf
     
  13. "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. As it turns out, the website wanted a different number of significant figures. Albeit, an incorrect number with the given information...
     
  15. Thank god
     
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