Homework # 5 EE517 Fall 2000 Due September 26, 2000
In Woodson & Melcher finish reading chapter 3 and chapter 5 section 5.1.
The iron's permeability may be assumed to be infinite.
a) Write Ampere's law for the above magnetic device.
b) What is the B field in the iron where the winding is?
c) What is the flux linked by the coil and the inductance?
The mean path length around the iron core is lm. The winding factor is k and the area of the window is Aw.
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 x must be less than a.
a) Write down the expression for conservation of energy for the electromagnet. Repeat the same for co-energy. What is the definition of co-energy in terms of the energy, flux and current?
b) What is the co-energy for the electromagnet?
c) What is the magnetic force on the iron ball? Is the force to up or down?
d) At what current will the net force of gravity and magnetic force be zero?