So, I kind of addressed this in Leeborg’s project post:
To elaborate more, the whole point of a “toroid” shaped coil is to contain the magnetic field, so that it does not create leakage current in surrounding metals or produce EMI for other circuit components. It’s designed to do the exact opposite of what we need. See how it’s made, thinking of the right-hand-rule?
If you look at the picture you in your previous post above, it shows “B=0” next to all the field lines. That means they’re confined and have no strength.