Spring EE321 10
Homework 1
Problem 1 Review of line-integral and application to MMF drop.
Consider a Cartesian co-ordinate system (x,y,z). Suppose a uniform H-field of 1 A/m
exists in the direction of the x-axis. Calculate the MMF drop from the point (1,1,1) to the
point (2,5,-1).
Problem 2 Review of line-integral and application to MMF drop.
Consider a Cartesian co-ordinate system on a plane (the plane lines on the x- and y-axis).
A current of 100 A is flowing up out of the plane at the origin. Find the MMF drop
between the point x=1,y=0 and the point x=3, y=2.
Problem 3 Review of surface integral and definition of flux.
Consider a Cartesian co-ordinate system (x,y,z). A uniform B-field of 1 T exists along
the direction of the x-axis. Now consider the rectangular plane bounded by the points
(1,0,0),(0,1,0),(0,1,1),(1,0,1). How much flux is traveling through the rectangular plane.
Problem 4 Review of surface integral, definition of flux, Gausses Law.
Consider a cone device shaped with a large end with a radius of 0.1 m, and a small end
with a radius of 0.03 m. The two ends are 2 m apart. A flux of 3 mWb enters the large
end. A flux of 2 mWb enters the solid through the side of the cone. The B-field leaving
the small end of the cone exists in a direction normal to the small end of the cone and is
uniform. What is the flux density leaving the small end ?
Problem 5 UI Inductor Analysis
Consider the UI core shown on Slide 34/35 of your Lecture Set 1 lecture handouts.
Consider the following parameters:
w =1
cm; ws = 5 cm; d s = 2 cm; d = 5 cm; g = 1 mm; N = 100
Suppose the material used is such that for a flux density less than 1.3 T (the saturation
point), the magnetic material is linear and has a permeability 1500 times that of free
space (i.e. a relative permeability of 1500).
What current will result in a flux density of 1.3 T ? (In other words, if we call this the
point of magnetic saturation, what current will saturate the core)