Induced emf in a square loop at rest

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SUMMARY

The induced electromotive force (emf) in a square loop at rest can be calculated using the formula emf = (μ₀I(a²))/(2π(a+b)b), where I(t) = (15.0 A)sin(2500t), a = 12.0 cm, and b = 15.0 cm. The discussion emphasizes the importance of applying both Ampere's law and Faraday's law to solve the problem effectively. The initial attempt to substitute the current directly into the emf equation was insufficient, highlighting the need for a comprehensive understanding of electromagnetic principles.

PREREQUISITES
  • Understanding of Faraday's law of electromagnetic induction
  • Familiarity with Ampere's law
  • Knowledge of electromagnetism concepts, particularly induced emf
  • Basic calculus for handling time-dependent functions
NEXT STEPS
  • Study the derivation and application of Faraday's law in various contexts
  • Explore the relationship between current and magnetic fields using Ampere's law
  • Investigate time-varying magnetic fields and their effects on induced emf
  • Practice problems involving induced emf in different geometries and configurations
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Students studying electromagnetism, physics educators, and anyone seeking to deepen their understanding of induced emf in electrical circuits.

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Homework Statement



Determine the emf induced in the square loop in the figure if the loop stays at rest and the current in the straight wire is given by I(t) = (15.0 A)sin(2500t) where t is in seconds. The distance a is 12.0 cm, and b is 15.0 cm.

Homework Equations



In the question prior to this one in the homework, emf=(uIv(a^2))/(2pi(a+b)b)



The Attempt at a Solution



I initially attempted to just substitute the equation for I into the emf equation but that hasn't worked. I'm clueless on how to proceed.

Please help! Thank you!
 

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This is not just an Ampere's law problem. Faraday's law also applies.

AM
 

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