Engineering What is the magnetic field of a half toroid?

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The discussion centers on determining the magnetic field of a half toroid, with initial thoughts on using Ampere's law and Biot-Savart's law. The user proposes that the magnetic field can be calculated as B = (μo * i) / r, but questions arise regarding the application of Biot-Savart's law due to symmetry potentially leading to a zero vector sum. Clarification is sought on the specifics of the half toroid configuration, including whether it is an air core and how it is cut. The complexity of the problem is acknowledged, indicating that a straightforward solution may not exist. The user is looking for guidance on correcting their approach and understanding the true magnetic field in this scenario.
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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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Thread 'Why wasn’t gravity included in the potential energy for this problem?'

Thread 'Why wasn’t gravity included in the potential energy for this problem?'

I’m looking at the attached vibration problem. The solution in the manual includes the spring potential energy but does NOT include the gravitational potential energy of the hanging mass. Can someone explain why gravitational potential energy is not included when deriving the equation of motion? I tried asking ChatGPT but kept going in circles and couldn't figure out. Thanks!
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