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M o d u le 8- ECE 2- Electro mag n etics.d o cx
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Module 9-10: Electromagnetics (ECE 2)
Introduction: A Del operator is widely used to interpret multi-dimensional differentiation in
different coordinate system. On this module, the students will understand concept of
divergent, curl, gradient and Laplacian operators.
Learning outcomes and Learning activities:
At the end of this topic, the students will be able to:
1. Discuss different mathematical model techniques involving divergent and curl
2. Compute parameters involving divergent and curl.
3. Compute parameters involving gradient and Laplacian.
The students are expected to perform the following learning activities.
1. Watch recorded lecture videos.
2. Attend online discussion.
3. Solving calculation problems.
4. Browse topic module.
Discussions
Del Operator
It is a simultaneous derivative of three dimensional spaces that is used in the interpretation of
divergent, curl, gradient and Laplacian operation. It is also called as “nabla” operator. In
symbol, consider the formula below for the Del operator involving rectangular coordinate
system.
Note that:
[2]
Divergent of a vector is a scalar quantity.
[2]
Curl of a vector is a vector quantity.
Gradient of a vector is a scalar quantity.
[2]
Laplacian of a vector is a vector quantity.
Table below show the formulas of the four operators in different coordinate system.
[2]
Given a vector field A. This can be expressed as A(x,y,z), A(ρ, φ,z) and A(r, Ɵ, φ) in different
coordinate system. Also note that the unit vector ax, ay and az can be expressed as i, j and k
notation.
Sample Problems:
[ 3 ]
1. Given a vector field F( x,y,z)= (x+y)ax+(y+z)ay+(x+z)az, determine the divergent of vector
field F. What is the value of the divergent of vector F at point:
a. P( 1,1,1)
b. Q(1,-1,1)
c. A at origin
2. Given a vector field F( ρ,φ,z)= 1/ρ aρ+2ρaφ+2az, determine the divergent of vector field F.
What is the value of the divergent of vector F at point:
d. A at origin
e. P(2, 30o,3)
3. Given a vector field F( r,Ɵ,φ)= rar+2aƟ - aφ, determine the divergent of vector field F. What
is the value of the divergent of vector F at point:
f. A at origin
g. Q(3, 30o, 60o)
4. Given a vector field C( x,y,z)= 2xax+2yay+2zaz, determine the curl of vector field C.
5. Determine the curl of vector field F( ρ,φ,z)= ρaρ+2aφ - az.
Summary, Life application and Biblical implication
Del operator or nabla operator is a basis in performing multi-dimensional derivatives of
different coordinate system. Divergent, curl, gradient and Laplacian are the operations based
on del operator.
Life application and thoughts to fonder: The net force between two charges is affected by the
distance between them. It will increase when the charges are near to each other and decreases
otherwise. God's love is a universal force that is not defined by distance; it is equally felt by
every human being!
References:
Hayt, W.H. (2006). Engineering Electromagnetics. (7th Edition). Boston: McGraw-Hill.
Kraus, J.D. (1999. Electromagnetics: with applications. (5th Edition). Boston: McGraw-Hill.
Demarest, K. (1998). Engineering Electromagnetics. New Jersey: Prentice Hall.