Question about magnetism/induced emf in small coil

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SUMMARY

The discussion centers on calculating the induced electromotive force (emf) in a small coil placed within a solenoid. The solenoid has a length of 25.0 cm, a radius of 1.60 cm, and 5500 turns, carrying a current of 1.50 A. The small coil, with a radius of 1.05 cm and 130 turns, experiences a change in magnetic flux from 14.4 x 10-6 Weber (WB) to 0 WB when the solenoid's current is switched off over 25 ms. The induced emf can be calculated using the formula: Induced EMF = -N (delta Φ / delta t).

PREREQUISITES
  • Understanding of electromagnetic induction principles
  • Familiarity with the formula for induced emf: Induced EMF = -N delta Φ / delta t
  • Knowledge of magnetic flux calculations, including B (magnetic field) and A (area)
  • Basic circuit theory, particularly regarding resistors and current flow
NEXT STEPS
  • Study the concept of magnetic flux and its calculation in different geometries
  • Learn about Faraday's Law of Electromagnetic Induction in detail
  • Explore the effects of changing magnetic fields on induced currents in coils
  • Investigate practical applications of induced emf in electrical engineering
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Students studying electromagnetism, physics educators, and electrical engineering professionals seeking to deepen their understanding of induced emf and magnetic flux concepts.

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Homework Statement


A solenoid with a length of 25.0 cm, radius 1.60 cm and 5500 turns carries a current of 1.50 A. A small coil of radius 1.05 cm and 130 turns is placed at the center of the solenoid with its axis in the same direction as that of the solenoid. A 470 ohms resistor is connected to the ends of the small coil. The current in the solenoid is switched off within 25 ms.

Determine the magnitude of the induced emf in the small coil.

Homework Equations



Induced EMF= -N delta \Phi / delta t

The Attempt at a Solution



The main problem I am having is figuring out the change of the magnetic flux. I figured out the magnetic flux through the small coil at 14.4 x10^-6 WB (from the equation magnetic flux=BA cos theta) but I don't know what it changes to or from.
 
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Since the current in the solenoid is switched off, it no longer produces a magnetic field. So the flux changes to 0 over the course of 25 ms.
 
so for delta \Phi it would be (14.4x10^-6)-(0)?
 

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