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Why is the magnetic field characterized in units of "Tesla" in the case of a solenoid, while it is typically characterized in terms of the "magnetic field integral" (so in $T\cdot m$) in the case of a toroid?

Example: The ATLAS experiment (an experiment at LHC) is made of two magnetic fields; one due to a solenoid and the other due to a toroid.

In the case of the specific toroid magnetic field, most descriptions characterise the magnetic field in Tesla∙meter ($T\cdot m$).

First example: https://cds.cern.ch/record/409763/files/cer-000336903.pdf

On page 842, second paragraph:

"The BT (meaning Barrel [central] Toroid) provides 2-6 T∙m while the ECT (meaning End-Cap [in forward region] Toroid) contributes with 4-8 T∙m"

Second example: http://opendata.atlas.cern/release/2020/documentation/atlas/experiment.html

"An extensive muon spectrometer with an air-core toroid magnet system surrounds the calorimeters. It includes three layers of high-precision tracking chambers. The field integral of the toroid magnets ranges from 2.0 to 6.0 Tm across most of the detector."

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    $\begingroup$ That doesn’t really make sense, clearly both situations have easily calculable magnetic fields. Can you quote from whatever reference says this? $\endgroup$
    – knzhou
    Aug 28, 2021 at 16:34
  • $\begingroup$ @knzhou : I have added more information and example. $\endgroup$
    – Mathieu Krisztian
    Aug 28, 2021 at 16:44
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    $\begingroup$ "The performance of the torojds in terms of bending power for muon detection is characterised by the field integral IBdl where B is the azimuthal field component and dl is a trajectory between the inner and outer radii of the toroids." I've copied this from your first reference. Clearly it accounts for the Tm unit, though I don't understand how to derive or apply the field integral. $\endgroup$
    – Philip Wood
    Aug 28, 2021 at 17:03
  • $\begingroup$ This is strange, because in the inner detector (solenoid magnetic field), the bending power for charged particle is also the magnetic field times the lenght of the trajectography inside this solenoid, so I don't see why for the solenoid, we don't characterize it as field times length. $\endgroup$
    – Mathieu Krisztian
    Aug 28, 2021 at 17:43

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