How Do You Calculate the Magnetic Field and Energy in a Solenoid?

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SUMMARY

The discussion focuses on calculating the magnetic field (B) and energy in a solenoid, specifically using the formula B = μ0 (N/L) I, where μ0 is the permeability of free space, N is the total number of loops, L is the length of the solenoid, and I is the electric current. Participants emphasize the need to apply Ampere's Law to derive the magnetic field and suggest using integrals to compute the total energy input required to establish the current. The conversation highlights the importance of understanding the relationship between electric fields and magnetic fields in electromagnetic theory.

PREREQUISITES
  • Understanding of Ampere's Law in electromagnetism
  • Familiarity with the concept of magnetic permeability (μ0)
  • Knowledge of integral calculus for energy calculations
  • Basic principles of solenoids and their properties
NEXT STEPS
  • Study the derivation of Ampere's Law and its applications in magnetic fields
  • Learn about the energy stored in magnetic fields and relevant integral calculations
  • Explore the properties of solenoids and their behavior in different configurations
  • Investigate the relationship between electric fields and magnetic fields in electromagnetic theory
USEFUL FOR

Students studying electromagnetism, physics educators, and anyone involved in electrical engineering or related fields seeking to understand solenoid behavior and energy calculations.

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Homework Statement



Consider a solenoid of length L, transverse area A, total number of loops N

Compute the magnetic field B inside the solenoid, assuming that it is uniform and vanishes outside the solenoid, neglect any boundary effects.

Working under the same assumptions, calculate the total energy input necessary to turn on an electric current through the solenoid from 0 to a final value I. This computation must involve an integral.

Homework Equations



I need to derive B = u0 (N/l) I for the first part.

The Attempt at a Solution



I don't really know where to start, that's really all i need is a starting point. I am a bit confused, so if someone knows which equations to use/or start with that would be a big help.

For example i had another problem where i had to compute the electric field E in a parallel plate capacitor...needed to derive E = Q/(\epsilon0A), but i had V=Ed, V=Q/C, and C = (\epsilon0A)/d to start with.
 
Last edited:
Physics news on Phys.org
Do you know Ampere's Law?
If so, think about what kind of path you'd need to use for it to be helpful.
 

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