# Example Problem - Toroid

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.

*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

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

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

Finally teh H_m can be calculated.

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

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## Points for page

Worth 117

Kirk total for paper 117 + 50 conference = 167