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Spencer Streeter
ECE 3300
Portfolio - 9/29/06-10/04/06
Portfolio #16 – 10/09/06
A = A xˆ + A yˆ + A zˆ
x

y
z
How do you find…
…a unit vector in the direction of A
1. Any vector can be made into a unit vector by dividing it by its length.
2. If given the starting point and ending point of a vector, subtract the ending point from the starting point, like
coordinates from like coordinates (i.e. (x2-x1, y2-y1, z2-z1)
3. Then divide each coefficient by the magnitude which is the square root of the sum of the squares.
A A
aˆ =   A
A A A
x
xˆ +
x
Ay
Ay
yˆ +
Az
zˆ
Az
…the magnitude of a vector
 for Cartesian Coordinates
1. Square each coefficient (Ax,Ay,Az)

2. Sum the squares
3. Take square root of sum.
A = A2x +A2y +A2z
 for Cross Product
1. Area of parallelogram

area = baseheight  = ABsin AB 
…the component of A along B
 The scalar product or dot product of two vectors A und B is defined as:
the projection of A onto B

which is to say the component of A along or parallel to B
A || B = A  B = ABcos  AB 
AB

B
= AcosAB 
…a vector parallel to A
1. Will have a dot product of 1.
 2. Will have a cross product of 0.
…a vector perpendicular to A,
1. Will have a dot product of 0.

2. Will have a cross product of 1.

A  B = ABcos  AB   1
A  B = ABsin AB   0
A  B = ABcos  AB   0
A  B = ABsin AB   1
…a vector parallel to a plane?
product with any vector in the plane is zero, it is parallel to plane.
1. Find a vector such that its cross

1-4
UNIVERSITY OF UTAH DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING
50 S. Central Campus Dr | Salt Lake City, UT 84112-9206 | Phone: (801) 581-6941 | Fax: (801) 581-5281 | www.ece.utah.edu
Spencer Streeter
ECE 3300
Portfolio - 9/29/06-10/04/06





1
AB


cos1
1
2. AB  2n  cos




A
B
A
B






…a vector perpendicular to a plane?
 Take cross product of plane defined by 2 vectors in the plane that are not parallel. (i.e. A and B)



 AB 
0

 cos1
1
  AB  n  cos





A B 
A B 

ˆ
 A  B = ABsin AB n


1. Find an equation that describes the plane (i.e 2x  3y  4z  16 )
2. Find 3 points corresponding to x,y, and z on the plane by plugging in values for the other 2 variables and
solving for 3rd. (Hint: use zero for other 2 values.) (i.e. P1  8,0,0, P2  0,16 3,0, P3  0,0,4 )
3.

How do you use vectors to sketch fields?



For each point in 2-D or 3-D space vectors as they are defined, will have a magnitude and direction. For example, if
we have an equation for E , it will be a vector that acts a s a function of x, y and z or whatever coordinate system
applies. As we “plug-in” different values of x, y, and z, a vector with a specific angle and magnitude will result.
Multiple points will form a “sketch” of fields comprised of vector components.
Assignment 
Ch.3-1,5a-c,6,7,15,17
Portfolio #17 – 10/11/06
How do you find…
total charge or current in line
1. For Charge on line
Q  v dV
V
refer to table 3-1 on page 118 of Ulaby text for dv
2.
For Current in a line
by…
 Current densisty is given
(A/m2)
J  v u
and Current by..
I

 J  ds
(A)
s
refer to table 3-1 on page 118 of Ulaby text for ds
total charge or current in a surface
1. See above

2. See above
total charge or current volume distributions
1. See above
2. See above
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UNIVERSITY OF UTAH DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING
50 S. Central Campus Dr | Salt Lake City, UT 84112-9206 | Phone: (801) 581-6941 | Fax: (801) 581-5281 | www.ece.utah.edu
Spencer Streeter
ECE 3300
Portfolio - 9/29/06-10/04/06
Ch4-1,4,5a,7,8
Portfolio #18 – 10/13/06
What is the electric field (physically)?
An electric field is the phenomenon that exerts a force on charged objects.
What causes it?
An electric field is due to net effect of multiple point charges.
How do you compute the electric field from point, line, surface, or volume charge distributions?
COULOMB’S LAW – STEP BY STEP
(Sorry.. for some reason by vector symbol is not working. )
1.
2.
Define an ORIGIN at a convenient point
Write the vector Rs from the ORIGIN to the SOURCE(s) (charge) location
If you used an origin at the center of the grid (0,0,0):
Rs  xs xˆ  ys yˆ  zszˆ
3.
Write the vector Rp from the ORIGIN to the location where you want to find the FIELD (field point).

4.
R p  x p xˆ  y p yˆ  z p zˆ
Apply Coulomb’s Law
a.
Write the vector from the SOURCE(s) to the FIELD
Rps = Rp - Rs
b.
Define the SOURCE (charge) distribution. (Note: This is a scalar.)
dq = l dl
(Line charge)
dl = dx, dy, or dz
(See p. 110 of text)
dl = dr, r d, dz
dl = dR, R d, Rsin d
dq = s ds
(Surface charge)
ds = dx dy, dy dz, or dx dz
ds = r ddz, drdz, r dr d
ds = R2sin d d, Rsin dR d, R dR d
dq = v dv
(Volume charge)
dv = dxdy dz
dv = r dr d dz
dv = R2sin dR d d
c.
Write the electric field caused by the charge distribution.
dE 
Rˆ ps 
dq
4 R ps
2
Rˆ ps 
dq
4 R ps
3
R ps
R ps
R ps
To find the magnitude of the vector: Take each
3-4
UNIVERSITY OF UTAH DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING
50 S. Central Campus Dr | Salt Lake City, UT 84112-9206 | Phone: (801) 581-6941 | Fax: (801) 581-5281 | www.ece.utah.edu
Spencer Streeter
ECE 3300
Portfolio - 9/29/06-10/04/06
vector component, square it, sum them, and take the square root.
|Rps| = sqrt (Rx2 + Ry2 + Rz2)
d.
Sum or integrate the sources to find the field.
E
endsource
endsource
startsource
startsource
 dE  
1
4 R ps
3
R ps dq
Note: E, Rps, dE are all vectors.
Ch.4-9 (second part of 4-9) ,10, 14, 15,19
4-4
UNIVERSITY OF UTAH DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING
50 S. Central Campus Dr | Salt Lake City, UT 84112-9206 | Phone: (801) 581-6941 | Fax: (801) 581-5281 | www.ece.utah.edu