Homework # 2 EE517 Fall 2000 Due September 7, 2000

Start reading chapter 2 in Woodson & Melcher

Problem 1

The potential in a given region is .

- What are the units of A?
- What is the electric field in the region?
- Do the line integral of the electric field from x=0, y=0 to x=L, y=L along path (a) in the figure below. Along each segment of the path give and the limits of integration.
- Do the line integral of the electric field from x=0, y=0 to x=L, y=L along path (b) in the figure below. What is and the limits of integration.
- Integrate the potential from x=0, y=0 to x=L, y=L. Compare your answers in c), d) and e).

Problem 2

The iron's core has the same cross section everywhere.

- Assuming the permeability of the iron is infinite, use Ampere's law to find the H field generated by the current. Draw the surface and the contour that encloses the surface that you use to apply Ampere's law. Indicate the unit normal to the surface and the direction of the line integral on your drawing. What is the B field? Give the units.
- Use Faraday's law to find the terminal voltage. Draw the surface and the contour that encloses the surface that you use to apply Faraday's law. Indicate the unit normal to the surface and the direction of the line integral on your drawing.
- What is l, f, and L? Give the units.
- Repeat the above to find B
_{g}, B_{Fe}, l, f, and L when the m in the iron is not infinite but rather some finite value. You may define 2l+2h-g = l_{c}, the core path length.

Problem 3

For the magnetic core above ht is 0.25 inches, OR = 2.5 inches, and IR = 1.5 inches. The relative permeability of the material is 100 and there are 50 turns wound on the core. Be sure to label your units. Obtain an exact solution taking advantage of the problem's symmetry.

a) If the winding current is 30 A dc, what are the maximum H field and the maximum B field in the core and where in the core do they occur? Where in the core is the field a minimum?

b) The saturation flux density of a common magnetic iron, 3.25 % SiFe, is 1.6 Tesla. At what current will the above core begin to saturate?

c) Draw the contour and surface for using Faraday's law to find the voltage at the terminals of this inductor.

d) What is the inductance of this inductor and what is the flux (l) linked by the winding with a current of 30A?

e) What is the voltage at the terminals of the winding for 30A dc and for 60Hz 30A peak ac?

f) What is the current density in the wire for 30A dc if you assume the wire occupies all the space available to it and you neglect the space between the different turns?

g) What do you think happens in a circuit when the core saturates, i.e. the B field becomes a constant value? What is the circuit model for the inductor in this case.