Homework # 10 EE517 Fall 2000 Due December 5, 2000

Read Chapter 8. Put the emphasis 8.3, 8.4, and 8.5.

Do 8.1, 8.4, and 8.8 in Woodson and Melcher

Problem 1 (Old final problem)

For the magnetic structure above g << d (you may assume g = 0), in the iron and there are N turns. You may assume the iron's cross sectional area is the same everywhere.

  1. What is H in the iron and in the air gap?
  2. What is the vector field in both air gaps (two expressions)? Note that the magnitude of the B field is the same in both air gaps.
  3. You are to find the force in the y direction on the movable plunger using the Maxwell stress tensor. Do not worry about fringing fields.

  4. Sketch the closed surface the stress tensor must be integrated over in order to find the force on the moveable plunger. Indicate the unit normal to the surface on your sketch.
  5. Find the contribution to the y directed force of the stress tensor on each face of your surface. For those surfaces where the force is zero, explain why.
  6. What is the total y directed force in terms of the current I? Is the force directed up or down? You must explain for credit.