Derive an expression for B inside a toroid.
Estimate B resulting from 1.00 A current flowing through our demonstation toroid. A label on the toroid indicates: 521 turns, cross-sectional area 1.25 cm2, outside diameter 10.12 cm, inside diameter 7.60 cm.
Please see pg. 739-740 of HRW for the derivation of B in a toroid.
From the result B = (mu0 i N)/(2 pi r), taking N = 521 and ravg = 4.43 cm, I find B = 2.35 mT.
Another approximation would come from using the average value of 1/r rather than r; <1/r>avg = 1/(4.34 cm), for B of 2.40 mT. No significant difference... The variation of B across the cross-sectional area of the toroid is about 14% plus/minus of this value, from inner diameter to outer diameter.