Derive an expression for B inside a toroid.
Estimate B resulting from 1.00 A current flowing through our demonstation solenoid. A label on the solenoid 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 solenoid.
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.
Thanks to Janusz for pointing out that my original solution used the diameter in place of
the radius in the solution.