What is the magnetic field of a half toroid?

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SUMMARY

The magnetic field of a half toroid can be analyzed using both Ampere's Law and Biot-Savart's Law. According to Ampere's Law, the magnetic field B can be expressed as B = (μo * i) / r, where μo is the permeability of free space, i is the current, and r is the radius. However, Biot-Savart's Law indicates that due to symmetry, the vector sum of all differential magnetic fields may result in a net field of zero. Understanding the configuration of the half toroid, such as whether it is an air core and the orientation of the cut, is crucial for accurate calculations.

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  • Understanding of Ampere's Law and its application in magnetic field calculations
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  • Knowledge of magnetic field concepts, including permeability of free space (μo)
  • Basic understanding of toroidal geometry and symmetry in physics
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  • Study the application of Ampere's Law in different geometrical configurations
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Homework Statement
What is the magnetic field of a half toroid?
Relevant Equations
Magnetic field of a toroid: μo*N*i / 2*pi*r
Hello,
I would like to know what is the magnetic field of a half toroid.

Would we use Ampere's law? So, considering that the integral is equal to BA, we would have BA = μo * i, then B = (μo * i) / r. But, using Biot-Savart's law, by symmetry, it seems that the vector sum of all the differential magnetic fields is zero.

What is the true answer for this problem? How can I find it? Where are my mistakes?

Thank you!
 
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Just to be certain: cut in half which way? Air core? This is likely not simple.
 
hutchphd said:
Just to be certain: cut in half which way? Air core? This is likely not simple.
I will show an image.
 

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