Time dependence of induced emf in a loop

  • Thread starter JonNash
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  • #1
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Homework Statement



A uniform magnetic field B is perpendicular to the plane of a circular wire loop of radius R. The magnitude of the field varies with time according to B=B0exp(-t/τ) where B0 and τ are constants. The time dependence of the induced emf in the loop is
a) exp(-t22)
b) 1+exp(-t22)
c) 1-exp(-t/τ)
d) -exp(-t/τ)

Homework Equations



emf=-dΘ/dt
Θ=∫B.dA

The Attempt at a Solution



εdt=-dΘ
∫εdt=-∫dΘ
∫εdt=-Θ
∫εdt=-∫B.dA
∫εdt=-B∏R2
∫εdt=-B0.exp(-t/τ)∏R2

So with this I guessed that the time dependence would be option d) -exp(-t/τ)
Is this the correct answer?
 

Answers and Replies

  • #2
TSny
Homework Helper
Gold Member
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Hello, JonNash.

The question asks for the time dependence of ε. So you need to find an expression for ε as a function of time.
 

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