Mutual Inductance in a solenoid

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SUMMARY

The discussion focuses on calculating the mutual inductance (M) of a solenoid with a time-varying current. The formula derived by the user, M = P*n1*n2*A/L, is incorrect. The correct approach involves using the formula M = (μ₀ * n1 * n2 * A) / L, where μ₀ represents the permeability of free space. The user is advised to consider the instantaneous current value when applying the formula.

PREREQUISITES
  • Understanding of mutual inductance concepts
  • Familiarity with solenoid physics
  • Knowledge of electromagnetic theory
  • Basic algebra for manipulating equations
NEXT STEPS
  • Study the derivation of mutual inductance formulas
  • Learn about the role of permeability (μ₀) in inductance calculations
  • Explore the effects of changing current on inductance
  • Investigate practical applications of solenoids in circuits
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Students studying electromagnetism, physics educators, and electrical engineering professionals looking to deepen their understanding of inductance in solenoids.

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Homework Statement


A long solenoid (black coil) with cross-sectional area A cm^2 and length L is wound with n1 turns of wire. A time-varying current i1 flows through this wire. A shorter coil (blue coil) with n2 turns of wire surrounds it. Use (uo)(m*kg/s^2*A^2)
1) Find the value M of the mutual inductance.

Note: The current in coil 1 is constantly changing. However, when using the hints it may help you to consider the instant at which the current in coil 1 is A.

I don't exactly know how to post the image

Homework Equations



I used the above equation

The Attempt at a Solution


I got M = P*n1*n2*A/L but it was wrong. Not sure where I went wrong. Any help would be appreciated
 
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