What Is the Range of Magnetic Field Values Inside a Toroid?

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Homework Help Overview

The discussion revolves around calculating the range of magnetic field values inside a toroid, given its dimensions and current. The subject area includes electromagnetism and magnetic fields.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to apply the formula for magnetic field strength but expresses uncertainty about the correct use of the inner and outer radii. Some participants question the assignment of maximum and minimum values to the inner and outer radii, suggesting a need for clarification on how the magnetic field strength varies with distance from the center of the toroid.

Discussion Status

Participants are exploring the relationship between the radius and the magnetic field strength, with some guidance provided regarding the inverse relationship of the magnetic field strength to the distance from the center. There is a lack of explicit consensus on the correct assignment of maximum and minimum values, but the discussion is actively engaging with the problem setup.

Contextual Notes

Participants are navigating assumptions about the geometry of the toroid and the implications for the magnetic field calculations. The original poster's confusion about the radius values indicates potential gaps in understanding the underlying principles of magnetic fields in toroidal structures.

Angie K.
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Homework Statement



A toroid has a 49.4-cm inner diameter and a 57.4-cm outer diameter. It carries a 23 A current in its 500 coils. Determine the range of values for B inside the toroid.

A) Bmaximum = ?
B) Bminimum = ?

Homework Equations



B = mu0/2pi * NI/r[/B]

The Attempt at a Solution


I tried plugging in the values from the problem but I am not sure where I am going wrong.

B minimum = Mu0 * 500 * 23 / 2 pi * (.494/2)

B maximum = Mu0 * 500 * 23 / 2 pi * (.572/2)

Am I doing something wrong with the radius? Is the B minimum not thre inner r and the maximum the outer r?
 
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Is the B minimum not the inner r and the maximum the outer r?

No it's the other way around.

http://physics.aalto.fi/pub/kurssit/Tfy-3.15xx/Tp_ohjeet/33en.pdf

..the magnetic field strength decreases inversely proportional to the distance from the torus center

If you divide by a smaller number (eg inner radius) you get a larger result (eg maximum B).
 
Yes.
 

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