Rate of Field Change for Induced Current of Loop


by tevatron1
Tags: emf, induced current, loop, magnetic flux
tevatron1
tevatron1 is offline
#1
Feb21-12, 11:14 AM
P: 11
1. The problem statement, all variables and given/known data

A single conducting loop of wire has an area of 8.010−2 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
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kushan
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#2
Feb21-12, 11:21 AM
P: 259
Quote Quote by tevatron1 View Post
1. The problem statement, all variables and given/known data




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).
[/b]
θ would not be 90 as Area vector and B make 0 angle
tevatron1
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#3
Feb21-12, 11:26 AM
P: 11
Quote Quote by kushan View Post
θ would not be 90 as Area vector and B make 0 angle
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?

kushan
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#4
Feb21-12, 11:31 AM
P: 259

Rate of Field Change for Induced Current of Loop


as as i know you are doing correctly ,
where are you stuck ?
tevatron1
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#5
Feb21-12, 11:32 AM
P: 11
Quote Quote by kushan View Post
as as i know you are doing correctly ,
where are you stuck ?
Mastering Physics tells me this is the wrong answer, though it does not give any explanation as to why.
kushan
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#6
Feb21-12, 11:33 AM
P: 259
what is " mastering physics "
tevatron1
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#7
Feb21-12, 11:35 AM
P: 11
Quote Quote by kushan View Post
what is " mastering physics "
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.
kushan
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#8
Feb21-12, 11:37 AM
P: 259
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
tevatron1
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#9
Feb21-12, 11:39 AM
P: 11
Quote Quote by kushan View Post
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
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.
kushan
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#10
Feb21-12, 11:44 AM
P: 259
I am sorry as I fail to help you further with this problem
technician
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#11
Feb21-12, 12:04 PM
P: 1,506
You know the resistance of the loop and you know the current so you should be able to find the induced emf
tevatron1
tevatron1 is offline
#12
Feb21-12, 12:12 PM
P: 11
"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.
tevatron1
tevatron1 is offline
#13
Feb21-12, 12:26 PM
P: 11
As it turns out, the website wanted a different number of significant figures. Albeit, an incorrect number with the given information...
kushan
kushan is offline
#14
Feb22-12, 12:26 AM
P: 259
Thank god


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