Homework # 7 EE517 Fall 2000 Due October 17, 2000
In Woodson & Melcher read chapter 5 section 5.1.
Do problem 5.1 in Woodson and Melcher.
In the above figure an electromagnet is being used to levitate an iron ball. The force of gravity Fg is down as shown and is equal to m*g where g is the constant gravitational acceleration. The inductance of the electromagnet depends on the position x of the iron ball. Do not worry about any other direction of movement other than the x direction. The inductance of the electromagnet has been measured for different ball positions and a mathematical function as been fitted to the data. For values of x that are of interest the inductance can be approximated as
Note that x must be greater than zero.
a) Plot the inductance as a function of position.
b) What is the electromagnet's co-energy in terms of x, Lo, a and the current?
c) What is the magnetic force on the iron ball?
In the figure below a magnetic elastic beam is free to vibrate in the +/- x direction as shown. The total air gap in the x direction is l. The permeability of the iron and beam may be approximated as infinite. You may assume the elastic beam has an effective mass M so the motion of the beam can be described by a differential equation that contains this mass and the spatial coordinate x. The elastic force due to the bending of the beam can be modeled as a spring force .