Mutual Induction of a solenoid and a coil

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SUMMARY

The discussion focuses on calculating the induced electromotive force (emf) in a single-turn circular loop caused by a long solenoid with specific parameters. The solenoid has 1780 turns, a radius of 0.0435 m, and a length of 0.850 m, while the loop has a radius of 0.235 m. The solenoid current decreases linearly from 6.12 A to 1.46 A over 0.230 seconds. The relevant equations for mutual inductance and induced emf are provided, but the user struggles to arrive at the correct answer despite applying the formulas correctly.

PREREQUISITES
  • Understanding of mutual inductance and its calculation using the formula M=N*∏*μ0*n*r^2
  • Knowledge of induced emf calculation using Vind = - N*∏*μ0*n*r^2 * di/dt
  • Familiarity with the concept of linear current change over time (di/dt)
  • Basic principles of electromagnetism, particularly in relation to solenoids and loops
NEXT STEPS
  • Review the calculation of mutual inductance for different configurations of coils
  • Study the effects of changing current on induced emf in electromagnetic systems
  • Explore the application of Faraday's Law of Electromagnetic Induction in practical scenarios
  • Investigate the role of resistance in circuits involving inductive components
USEFUL FOR

Students studying electromagnetism, physics educators, and anyone involved in electrical engineering or circuit design who seeks to understand the principles of mutual induction and induced emf calculations.

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Homework Statement



A single-turn circular loop of radius R = 0.235 m is coaxial with a long 1780 turn solenoid of radius 0.0435 m and length 0.850 m, as seen in the figure below. The variable resistor is changed so that the solenoid current decreases linearly from 6.12 A to 1.46 A in 0.230 s. Calculate the induced emf in the circular loop. (The field just outside the solenoid is small enough to be negligible.)

Homework Equations



M=N*∏*μ0*n*r^2

Vind = - N*∏*μ0*n*r^2 * di/dt

di/dt=(1.46-6.12)/0.23

The Attempt at a Solution



I used mutual inductance equ to find the potential difference induced

N is 1780, n=N/length, r=0.0435

but I still can't get the correct answer. I don't know where I did wrong here. Does anybody help me to find the answer? Thank you
 

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Does anyone can help me?
 

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