## PHYS208 Fundamentals of Physics II

### Quiz 8 -- Ampere's Law

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 cm^{2},
outside diameter 10.12 cm, inside diameter 7.60 cm.

**Solution:**
Please see pg. 739-740 of *HRW* for the derivation of **B** in a toroid.

From the result *B* = (*mu*_{0} i N)/(*2 pi r*),
taking *N* = 521 and *r*_{avg} = 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.

"http://www.physics.udel.edu/~watson/phys208/quiz8soln.html"

Last updated April 24, 1998.

Copyright George Watson, Univ. of Delaware, 1998.