How Does Magnetic Flux and Peak EMF Relate in a Solenoid-Coil System?

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SUMMARY

The discussion focuses on calculating the magnetic flux and peak electromotive force (emf) in a solenoid-coil system. The solenoid has a radius of 15 cm, 5x10^7 turns per meter, and carries a current of 16A. The coil, consisting of 5 square turns with a side length of 5 cm, is coaxial with the solenoid. The magnetic flux through each loop of the coil is determined to be 2.5 Weber, and the peak emf induced in the coil due to a varying current in the solenoid is derived from the equation for magnetic field B, which is μ₀*n*I.

PREREQUISITES
  • Understanding of electromagnetic theory, specifically solenoids and coils.
  • Familiarity with the concept of magnetic flux and its calculation.
  • Knowledge of Faraday's law of electromagnetic induction.
  • Basic proficiency in using equations involving magnetic fields and currents.
NEXT STEPS
  • Study the derivation of the magnetic field inside a solenoid using the formula B = μ₀*n*I.
  • Learn about Faraday's law and how to calculate induced emf in varying magnetic fields.
  • Explore the relationship between magnetic flux and induced emf in different coil configurations.
  • Investigate the effects of varying current on magnetic fields and induced voltages in electromagnetic systems.
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Students and professionals in physics, electrical engineering, and anyone interested in understanding electromagnetic induction in solenoid-coil systems.

champ0342
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A coil is located at the center of a long solenoid of radius R = 15cm which has 5x10^7 turns per meter and carries a current I = 16A. The coil is coaxial with the solenoid and consists of 5 turns of wire each in the shape of a square of length a = 5cm on each side.What is the magnetic flux passing through each loop of the coil? If the current in the solenoid is not constan but varies as I=Im cos wt, where I am = 16A and w = 10rad/sec, find the peak emf induced in the coil.



I would like to offer relevant equations but I don't think I have any. I have tried the equations I thought were relevant without coming up with the correct equation



flux = NiA -> 16*.05*5=4 but the correct answer is 2.5. I haven't even got a clue about peak emf...
 
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Magnetic field B at the center of a long solenoid is mu_0*n*I, where mu_0 = 4*pi*10^-7. And flux = B*A
 

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