Example Problem - Toroid

From Class Wiki
Jump to: navigation, search

By: Kirk Betz

Problem: Concerning Ampere's law Let look at a coil around a toroid shown in the figure below. The coil has N = 20 turns around the toroid. The toroid has an inside diameter of ID = 4 cm and an outside diameter OD = 5 cm. Determine the field intensity H along the mean path length within the toroid with a current i = 2.5 A.

Toroid.jpg


Figure created by Kirk Betz


Solution:

Do symmetry the magnetic field intensity Hm along a circular contour within the toroid is constant. We can find the mean radius by


r_m=(\frac{1}{2})\frac{OD + ID}{2} = 2.25\ cm

Using the mean radius the mean path of length l_m can be calculated.


 l_m = { 2 \pi r_m} = 0.141\

With Ampere's Law (below) the field intensity along the mean path can be Found.

H_m=(\frac{Ni}{l_m})

Finally teh H_m can be calculated.

H_m=\frac{20 x 2.5}{.141}= 354.6\ A /m)

Since the width of the toroid is much smaller than the mean radius r_m we can assume a uniform H_m throughout teh cross-section of the toroid.

Reviewed by

Will Griffith

Matthew Fetke

Read by

Points for page

Worth 117

Kirk total for paper 117 + 50 conference = 167