![Page 1: Electromagnetic Theory (TE-232) - umartalhaumartalha.weebly.com/uploads/8/3/8/2/8382263/lecture4.pdf · Electromagnetic Theory (TE-232) Lecture by: Mr. Shakir Karim Buksh Assistant](https://reader034.vdocument.in/reader034/viewer/2022052500/5f10d2797e708231d44afb8c/html5/thumbnails/1.jpg)
Electromagnetic Theory (TE-232)
Lecture by:Mr. Shakir Karim Buksh
Assistant ProfessorTelecommunication Engineering Department
SSUET/QR/111
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Vector Calculus
SSUET/QR/111
Lecture 4
By: Shakir Karim BukshTelecommunication Engineering Department
2
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SSUET/QR/111
Differential Length, Area & Volume
By: Shakir Karim BukshTelecommunication Engineering Department
3
Differential Elements in length, area & volume
are useful in Vector Calculus.
We are defining them for
•Cartesian Coordinate System
•Circular Cylindrical System
•Spherical System
![Page 4: Electromagnetic Theory (TE-232) - umartalhaumartalha.weebly.com/uploads/8/3/8/2/8382263/lecture4.pdf · Electromagnetic Theory (TE-232) Lecture by: Mr. Shakir Karim Buksh Assistant](https://reader034.vdocument.in/reader034/viewer/2022052500/5f10d2797e708231d44afb8c/html5/thumbnails/4.jpg)
Cartesian Coordinate System
SSUET/QR/111
4By: Shakir Karim BukshTelecommunication Engineering Department
![Page 5: Electromagnetic Theory (TE-232) - umartalhaumartalha.weebly.com/uploads/8/3/8/2/8382263/lecture4.pdf · Electromagnetic Theory (TE-232) Lecture by: Mr. Shakir Karim Buksh Assistant](https://reader034.vdocument.in/reader034/viewer/2022052500/5f10d2797e708231d44afb8c/html5/thumbnails/5.jpg)
Cartesian Coordinate System (contd/2)
SSUET/QR/111
5By: Shakir Karim BukshTelecommunication Engineering Department
![Page 6: Electromagnetic Theory (TE-232) - umartalhaumartalha.weebly.com/uploads/8/3/8/2/8382263/lecture4.pdf · Electromagnetic Theory (TE-232) Lecture by: Mr. Shakir Karim Buksh Assistant](https://reader034.vdocument.in/reader034/viewer/2022052500/5f10d2797e708231d44afb8c/html5/thumbnails/6.jpg)
Cartesian Coordinate System (contd/3)
SSUET/QR/111
6By: Shakir Karim Buksh
Telecommunication Engineering Department
![Page 7: Electromagnetic Theory (TE-232) - umartalhaumartalha.weebly.com/uploads/8/3/8/2/8382263/lecture4.pdf · Electromagnetic Theory (TE-232) Lecture by: Mr. Shakir Karim Buksh Assistant](https://reader034.vdocument.in/reader034/viewer/2022052500/5f10d2797e708231d44afb8c/html5/thumbnails/7.jpg)
Cylindrical Coordinate System
SSUET/QR/111
7By: Shakir Karim Buksh
Telecommunication Engineering Department
![Page 8: Electromagnetic Theory (TE-232) - umartalhaumartalha.weebly.com/uploads/8/3/8/2/8382263/lecture4.pdf · Electromagnetic Theory (TE-232) Lecture by: Mr. Shakir Karim Buksh Assistant](https://reader034.vdocument.in/reader034/viewer/2022052500/5f10d2797e708231d44afb8c/html5/thumbnails/8.jpg)
Cylindrical Coordinate System (contd/2)
SSUET/QR/111
8By: Shakir Karim BukshTelecommunication Engineering Department
![Page 9: Electromagnetic Theory (TE-232) - umartalhaumartalha.weebly.com/uploads/8/3/8/2/8382263/lecture4.pdf · Electromagnetic Theory (TE-232) Lecture by: Mr. Shakir Karim Buksh Assistant](https://reader034.vdocument.in/reader034/viewer/2022052500/5f10d2797e708231d44afb8c/html5/thumbnails/9.jpg)
Cylindrical Coordinate System (contd/3)
SSUET/QR/111
9By: Shakir Karim BukshTelecommunication Engineering Department
![Page 10: Electromagnetic Theory (TE-232) - umartalhaumartalha.weebly.com/uploads/8/3/8/2/8382263/lecture4.pdf · Electromagnetic Theory (TE-232) Lecture by: Mr. Shakir Karim Buksh Assistant](https://reader034.vdocument.in/reader034/viewer/2022052500/5f10d2797e708231d44afb8c/html5/thumbnails/10.jpg)
Cylindrical Coordinate System (contd/3)
SSUET/QR/111
10By: Shakir Karim BukshTelecommunication Engineering Department
![Page 11: Electromagnetic Theory (TE-232) - umartalhaumartalha.weebly.com/uploads/8/3/8/2/8382263/lecture4.pdf · Electromagnetic Theory (TE-232) Lecture by: Mr. Shakir Karim Buksh Assistant](https://reader034.vdocument.in/reader034/viewer/2022052500/5f10d2797e708231d44afb8c/html5/thumbnails/11.jpg)
Cylindrical Coordinate System (contd/3)
SSUET/QR/111
11By: Shakir Karim BukshTelecommunication Engineering Department
![Page 12: Electromagnetic Theory (TE-232) - umartalhaumartalha.weebly.com/uploads/8/3/8/2/8382263/lecture4.pdf · Electromagnetic Theory (TE-232) Lecture by: Mr. Shakir Karim Buksh Assistant](https://reader034.vdocument.in/reader034/viewer/2022052500/5f10d2797e708231d44afb8c/html5/thumbnails/12.jpg)
Cylindrical Coordinate System (contd/4)
SSUET/QR/111
12By: Shakir Karim BukshTelecommunication Engineering Department
![Page 13: Electromagnetic Theory (TE-232) - umartalhaumartalha.weebly.com/uploads/8/3/8/2/8382263/lecture4.pdf · Electromagnetic Theory (TE-232) Lecture by: Mr. Shakir Karim Buksh Assistant](https://reader034.vdocument.in/reader034/viewer/2022052500/5f10d2797e708231d44afb8c/html5/thumbnails/13.jpg)
Cylindrical Coordinate System (contd/4)
SSUET/QR/111
13By: Shakir Karim BukshTelecommunication Engineering Department
![Page 14: Electromagnetic Theory (TE-232) - umartalhaumartalha.weebly.com/uploads/8/3/8/2/8382263/lecture4.pdf · Electromagnetic Theory (TE-232) Lecture by: Mr. Shakir Karim Buksh Assistant](https://reader034.vdocument.in/reader034/viewer/2022052500/5f10d2797e708231d44afb8c/html5/thumbnails/14.jpg)
Cylindrical Coordinate System (contd/4)
SSUET/QR/111
14By: Shakir Karim BukshTelecommunication Engineering Department
![Page 15: Electromagnetic Theory (TE-232) - umartalhaumartalha.weebly.com/uploads/8/3/8/2/8382263/lecture4.pdf · Electromagnetic Theory (TE-232) Lecture by: Mr. Shakir Karim Buksh Assistant](https://reader034.vdocument.in/reader034/viewer/2022052500/5f10d2797e708231d44afb8c/html5/thumbnails/15.jpg)
Cylindrical Coordinate System (contd/4)
SSUET/QR/111
15By: Shakir Karim BukshTelecommunication Engineering Department
![Page 16: Electromagnetic Theory (TE-232) - umartalhaumartalha.weebly.com/uploads/8/3/8/2/8382263/lecture4.pdf · Electromagnetic Theory (TE-232) Lecture by: Mr. Shakir Karim Buksh Assistant](https://reader034.vdocument.in/reader034/viewer/2022052500/5f10d2797e708231d44afb8c/html5/thumbnails/16.jpg)
Cylindrical Coordinate System (contd/4)
SSUET/QR/111
16By: Shakir Karim BukshTelecommunication Engineering Department
![Page 17: Electromagnetic Theory (TE-232) - umartalhaumartalha.weebly.com/uploads/8/3/8/2/8382263/lecture4.pdf · Electromagnetic Theory (TE-232) Lecture by: Mr. Shakir Karim Buksh Assistant](https://reader034.vdocument.in/reader034/viewer/2022052500/5f10d2797e708231d44afb8c/html5/thumbnails/17.jpg)
Cylindrical Coordinate System (contd/4)
SSUET/QR/111
17By: Shakir Karim BukshTelecommunication Engineering Department
![Page 18: Electromagnetic Theory (TE-232) - umartalhaumartalha.weebly.com/uploads/8/3/8/2/8382263/lecture4.pdf · Electromagnetic Theory (TE-232) Lecture by: Mr. Shakir Karim Buksh Assistant](https://reader034.vdocument.in/reader034/viewer/2022052500/5f10d2797e708231d44afb8c/html5/thumbnails/18.jpg)
Cylindrical Coordinate System (contd/4)
SSUET/QR/111
18By: Shakir Karim BukshTelecommunication Engineering Department
![Page 19: Electromagnetic Theory (TE-232) - umartalhaumartalha.weebly.com/uploads/8/3/8/2/8382263/lecture4.pdf · Electromagnetic Theory (TE-232) Lecture by: Mr. Shakir Karim Buksh Assistant](https://reader034.vdocument.in/reader034/viewer/2022052500/5f10d2797e708231d44afb8c/html5/thumbnails/19.jpg)
Cylindrical Coordinate System (contd/4)
SSUET/QR/111
19By: Shakir Karim BukshTelecommunication Engineering Department
![Page 20: Electromagnetic Theory (TE-232) - umartalhaumartalha.weebly.com/uploads/8/3/8/2/8382263/lecture4.pdf · Electromagnetic Theory (TE-232) Lecture by: Mr. Shakir Karim Buksh Assistant](https://reader034.vdocument.in/reader034/viewer/2022052500/5f10d2797e708231d44afb8c/html5/thumbnails/20.jpg)
Cylindrical Coordinate System (contd/4)
SSUET/QR/111
20By: Shakir Karim BukshTelecommunication Engineering Department
![Page 21: Electromagnetic Theory (TE-232) - umartalhaumartalha.weebly.com/uploads/8/3/8/2/8382263/lecture4.pdf · Electromagnetic Theory (TE-232) Lecture by: Mr. Shakir Karim Buksh Assistant](https://reader034.vdocument.in/reader034/viewer/2022052500/5f10d2797e708231d44afb8c/html5/thumbnails/21.jpg)
Cylindrical Coordinate System (contd/4)
SSUET/QR/111
21By: Shakir Karim BukshTelecommunication Engineering Department
![Page 22: Electromagnetic Theory (TE-232) - umartalhaumartalha.weebly.com/uploads/8/3/8/2/8382263/lecture4.pdf · Electromagnetic Theory (TE-232) Lecture by: Mr. Shakir Karim Buksh Assistant](https://reader034.vdocument.in/reader034/viewer/2022052500/5f10d2797e708231d44afb8c/html5/thumbnails/22.jpg)
Spherical Coordinate System
SSUET/QR/111
22By: Shakir Karim BukshTelecommunication Engineering Department
![Page 23: Electromagnetic Theory (TE-232) - umartalhaumartalha.weebly.com/uploads/8/3/8/2/8382263/lecture4.pdf · Electromagnetic Theory (TE-232) Lecture by: Mr. Shakir Karim Buksh Assistant](https://reader034.vdocument.in/reader034/viewer/2022052500/5f10d2797e708231d44afb8c/html5/thumbnails/23.jpg)
Spherical Coordinate System
SSUET/QR/111
23By: Shakir Karim BukshTelecommunication Engineering Department
![Page 24: Electromagnetic Theory (TE-232) - umartalhaumartalha.weebly.com/uploads/8/3/8/2/8382263/lecture4.pdf · Electromagnetic Theory (TE-232) Lecture by: Mr. Shakir Karim Buksh Assistant](https://reader034.vdocument.in/reader034/viewer/2022052500/5f10d2797e708231d44afb8c/html5/thumbnails/24.jpg)
Spherical Coordinate System
SSUET/QR/111
24By: Shakir Karim BukshTelecommunication Engineering Department
![Page 25: Electromagnetic Theory (TE-232) - umartalhaumartalha.weebly.com/uploads/8/3/8/2/8382263/lecture4.pdf · Electromagnetic Theory (TE-232) Lecture by: Mr. Shakir Karim Buksh Assistant](https://reader034.vdocument.in/reader034/viewer/2022052500/5f10d2797e708231d44afb8c/html5/thumbnails/25.jpg)
Spherical Coordinate System (contd/2)
SSUET/QR/111
25By: Shakir Karim BukshTelecommunication Engineering Department
![Page 26: Electromagnetic Theory (TE-232) - umartalhaumartalha.weebly.com/uploads/8/3/8/2/8382263/lecture4.pdf · Electromagnetic Theory (TE-232) Lecture by: Mr. Shakir Karim Buksh Assistant](https://reader034.vdocument.in/reader034/viewer/2022052500/5f10d2797e708231d44afb8c/html5/thumbnails/26.jpg)
Spherical Coordinate System (contd/2)
SSUET/QR/111
26By: Shakir Karim BukshTelecommunication Engineering Department
![Page 27: Electromagnetic Theory (TE-232) - umartalhaumartalha.weebly.com/uploads/8/3/8/2/8382263/lecture4.pdf · Electromagnetic Theory (TE-232) Lecture by: Mr. Shakir Karim Buksh Assistant](https://reader034.vdocument.in/reader034/viewer/2022052500/5f10d2797e708231d44afb8c/html5/thumbnails/27.jpg)
Differential Length, Surface Area and Volume elements for each geometry
SSUET/QR/111
27By: Shakir Karim BukshTelecommunication Engineering Department
![Page 28: Electromagnetic Theory (TE-232) - umartalhaumartalha.weebly.com/uploads/8/3/8/2/8382263/lecture4.pdf · Electromagnetic Theory (TE-232) Lecture by: Mr. Shakir Karim Buksh Assistant](https://reader034.vdocument.in/reader034/viewer/2022052500/5f10d2797e708231d44afb8c/html5/thumbnails/28.jpg)
SSUET/QR/111
Line, Surface & Volume Integrals
By: Shakir Karim BukshTelecommunication Engineering Department
28
The line integral is the integral of the tangential component of A
along curve L.
where,
A is the vector field,
L is the curve.
![Page 29: Electromagnetic Theory (TE-232) - umartalhaumartalha.weebly.com/uploads/8/3/8/2/8382263/lecture4.pdf · Electromagnetic Theory (TE-232) Lecture by: Mr. Shakir Karim Buksh Assistant](https://reader034.vdocument.in/reader034/viewer/2022052500/5f10d2797e708231d44afb8c/html5/thumbnails/29.jpg)
SSUET/QR/111
Line, Surface & Volume Integrals
By: Shakir Karim BukshTelecommunication Engineering Department
29
The line integral is the integral of the tangential component of A
along curve L.
where,
A is the vector field,
L is the curve.
The closed contour integral is
the path of integration of the closed curve
(aka circulation of A around L)
![Page 30: Electromagnetic Theory (TE-232) - umartalhaumartalha.weebly.com/uploads/8/3/8/2/8382263/lecture4.pdf · Electromagnetic Theory (TE-232) Lecture by: Mr. Shakir Karim Buksh Assistant](https://reader034.vdocument.in/reader034/viewer/2022052500/5f10d2797e708231d44afb8c/html5/thumbnails/30.jpg)
SSUET/QR/111
Line, Surface & Volume Integrals
By: Shakir Karim BukshTelecommunication Engineering Department
30
![Page 31: Electromagnetic Theory (TE-232) - umartalhaumartalha.weebly.com/uploads/8/3/8/2/8382263/lecture4.pdf · Electromagnetic Theory (TE-232) Lecture by: Mr. Shakir Karim Buksh Assistant](https://reader034.vdocument.in/reader034/viewer/2022052500/5f10d2797e708231d44afb8c/html5/thumbnails/31.jpg)
SSUET/QR/111
Line, Surface & Volume Integrals
By: Shakir Karim BukshTelecommunication Engineering Department
31
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SSUET/QR/111
Line, Surface & Volume Integrals
By: Shakir Karim BukshTelecommunication Engineering Department
32
NOTE:
a closed path defines an open surface as shown in Figure 3.11
![Page 33: Electromagnetic Theory (TE-232) - umartalhaumartalha.weebly.com/uploads/8/3/8/2/8382263/lecture4.pdf · Electromagnetic Theory (TE-232) Lecture by: Mr. Shakir Karim Buksh Assistant](https://reader034.vdocument.in/reader034/viewer/2022052500/5f10d2797e708231d44afb8c/html5/thumbnails/33.jpg)
SSUET/QR/111
Line, Surface & Volume Integrals
By: Shakir Karim BukshTelecommunication Engineering Department
33
NOTE:
a closed path defines an open surface as shown in Figure 3.11
whereas
a closed surface defines a volume as depicted in Figure 3.16
![Page 34: Electromagnetic Theory (TE-232) - umartalhaumartalha.weebly.com/uploads/8/3/8/2/8382263/lecture4.pdf · Electromagnetic Theory (TE-232) Lecture by: Mr. Shakir Karim Buksh Assistant](https://reader034.vdocument.in/reader034/viewer/2022052500/5f10d2797e708231d44afb8c/html5/thumbnails/34.jpg)
SSUET/QR/111
Line, Surface & Volume Integrals
By: Shakir Karim BukshTelecommunication Engineering Department
34
NOTE:
a closed path defines an open surface as shown in Figure 3.11
whereas
a closed surface defines a volume as depicted in Figure 3.16
![Page 35: Electromagnetic Theory (TE-232) - umartalhaumartalha.weebly.com/uploads/8/3/8/2/8382263/lecture4.pdf · Electromagnetic Theory (TE-232) Lecture by: Mr. Shakir Karim Buksh Assistant](https://reader034.vdocument.in/reader034/viewer/2022052500/5f10d2797e708231d44afb8c/html5/thumbnails/35.jpg)
SSUET/QR/111
Line, Surface & Volume Integrals
By: Shakir Karim BukshTelecommunication Engineering Department
35
![Page 36: Electromagnetic Theory (TE-232) - umartalhaumartalha.weebly.com/uploads/8/3/8/2/8382263/lecture4.pdf · Electromagnetic Theory (TE-232) Lecture by: Mr. Shakir Karim Buksh Assistant](https://reader034.vdocument.in/reader034/viewer/2022052500/5f10d2797e708231d44afb8c/html5/thumbnails/36.jpg)
SSUET/QR/111
The Next Lecture will be on
differentiation of Vectors
By: Shakir Karim BukshTelecommunication Engineering Department
36