Find the EMF in the loop as a function of time.

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SUMMARY

The discussion focuses on calculating the electromotive force (emf) in a loop as a function of time, utilizing the equation for induced emf, which is defined as emf = -dΦ/dt. The magnetic flux (Φ) is expressed as the integral of the magnetic field (B) over the area (A) of the loop, specifically Φ = ∫B · dA. The process involves two steps: first, evaluating the integral to determine the magnetic flux as a function of time, and second, differentiating this flux with respect to time to find the induced emf.

PREREQUISITES
  • Understanding of electromagnetic fields and their properties
  • Familiarity with calculus, specifically integration and differentiation
  • Knowledge of the concepts of magnetic flux and induced emf
  • Proficiency in using the equation E=hv for energy calculations
NEXT STEPS
  • Study the principles of electromagnetic induction and Faraday's Law
  • Learn how to compute magnetic flux for different geometries
  • Explore the relationship between magnetic fields and electric currents
  • Investigate applications of induced emf in real-world scenarios, such as generators
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone interested in understanding electromagnetic induction and its applications in electrical engineering.

ugobroncs3343
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Homework Statement



electromagnetic field

Homework Equations



E=hv

The Attempt at a Solution



I know that t is the variable and h1 and h2 I and I2 are considered given all we are doing is doing the algebra set up but not sure how to show this exactly.?
 

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Recall the definition of the induced emf,

[itex]\text{emf} = - \frac{d\Phi}{dt},[/itex]

where the magnetic flux is defined as

[itex]\Phi = \int \vec{B} \cdot d\vec{A}.[/itex]

Your goal is to find the flux as a function of time (clearly it is a function of time, since the area of the loop is growing with time), and then insert that into the formula for the induced emf. So it's a two step process: evaluate the integral to obtain the flux, and then take its time derivative.
 

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