# HW7 - ECE 134 Introductory Field Theory Fall 2010 Reading...

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ECE 134 Introductory Field Theory Fall 2010 Page 1 of 2 Reading Assignment: Cheng: Chapters 6-7 Homework #7 Due: Monday 15 November 2010 1) The toroid shown below uses an annular core of high-permeability material with a square cross section. The average radius of the toroid is a , and N turns of wire carrying a current I wrap around the core. A small section of the core is removed to form an air-gap of height g as shown. a. Use an equivalent magnetic circuit to find an expression for the magnetic flux in the gap. Assume that the flux is uniformly distributed throughout the toroid cross section, and that the reluctance of the core is negligible in comparison to the gap. b. Find an expression for the magnetic field H in the air gap. c. Find an expression for the self-inductance of this toroid. 2) Do P.6-52 in Cheng 3) Do P.6-53 in Cheng. Hint: first find the inductance as a function of x using the long- solenoid approximation.

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