What is the relationship between induced emfs and circuit shape in a solenoid?

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SUMMARY

The relationship between induced electromotive forces (emfs) and circuit shape in a solenoid is crucial for understanding electromagnetic induction. When a circuit encircles a long solenoid with a changing current, an induced emf of 360 V can be observed, leading to a potential difference of 359 V across a resistor positioned at a 1-degree angle from the solenoid's center. However, the circuit's shape and the resistance must be considered, as high resistance is necessary to ensure that the induced current remains insignificant, and self-inductance effects can influence the calculations. Therefore, the shape of the circuit does indeed matter in these scenarios.

PREREQUISITES
  • Understanding of electromagnetic induction principles
  • Knowledge of solenoid characteristics and behavior
  • Familiarity with induced emf calculations
  • Concept of self-inductance in electrical circuits
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  • Study the principles of electromagnetic induction in detail
  • Learn about the effects of self-inductance on circuit behavior
  • Explore advanced topics in circuit design around solenoids
  • Investigate the mathematical modeling of induced emf in varying circuit shapes
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Physics students, electrical engineers, and educators looking to deepen their understanding of electromagnetic principles and improve teaching methods in introductory physics courses.

TheLil'Turkey
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So if a circuit goes once around an extremely long solenoid whose changing current causes an induced emf of 360 V (in the circuit) at a particular time, does that mean that regardless of the shape of the circuit, the induced emf will be 1 V per degree? If the circuit has only one resistor whose beginning and end make a 1 degree angle with the center of the solenoid, does that mean that the potential difference across that resistor is 359 V at that moment in time?
 
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That's right, provided the circuit path is close to the solenoid relative to its length.

[edit]... another qualifier, the resistance needs to be high enough so that the induced current is insignificant. There's a self inductance effect in the circuit, and for that calculation, shape DOES matter.
 
Last edited:
jambaugh said:
That's right, provided the circuit path is close to the solenoid relative to its length.

[edit]... another qualifier, the resistance needs to be high enough so that the induced current is insignificant. There's a self inductance effect in the circuit, and for that calculation, shape DOES matter.
Oh ya! I didn't think about self-inductance; I think that's the next thing I learn about. Thank you.

This should be taught better in 1st year physics courses.
 

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