How Do You Calculate Induced EMF in a Loop Near a Time-Varying Current?

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SUMMARY

The discussion focuses on calculating the induced electromotive force (e.m.f.) in a rectangular loop placed near a wire with a time-varying current described by the equation it=2.92 + 1.19t². The loop dimensions are a=1.80 cm and b=2.10 cm, with a distance d=0.290 cm from the wire. The magnetic flux through the loop at t=2.50 seconds is calculated as 8.59×10-8 T·m². To find the induced e.m.f., participants are directed to apply Maxwell's Equations, specifically focusing on the rate of change of magnetic flux.

PREREQUISITES
  • Understanding of Maxwell's Equations
  • Knowledge of magnetic flux calculations
  • Familiarity with electromotive force (e.m.f.) concepts
  • Basic calculus for rate of change computations
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  • Study the application of Faraday's Law of Induction
  • Learn about calculating magnetic flux in varying magnetic fields
  • Explore the implications of time-varying currents on magnetic fields
  • Investigate the relationship between current, magnetic fields, and induced e.m.f.
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help me how to solve this problem ??(e.m.f)

A rectangular loop with sides of length a= 1.80 cm and b= 2.10 cm is placed near a wire that carries a current that varies as a function of time: it=2.92 + 1.19t2 where the current is in Amperes and the time is in seconds. The distance from the straight wire to the closest side of the loop is d= 0.290 cm.

the figure is here : http://img171.imageshack.us/img171/5849/prob09awloop2aa6.gif


1) What is the magnetic flux through the loop at time t= 2.50 seconds? (Define positive flux into the page.)

my answer is :

(mu0*I/2*pi)*b*ln[(d+a)/d]
=8.59×10-8 T*m^2


2) What is the induced e.m.f. in the loop at time t= 2.50 seconds?
(Note that positive emf is clockwise. Compute the rate of change of magnetic flux through the loop to get the e.m.f.. )

help me how to solve this problem ??
 
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What's the rate of change of magnetic flux through the loop? You can use your expression from part 1.
 


HINT: Maxwell's Equations... which equation has something regarding the change in magnetic flux?
 

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