Post on 02-May-2023
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Electromagnetics:
Electromagnetic Field Theory
Differential Length, Area & Volume
Outline
•Cartesian Coordinates•Cylindrical Coordinates• Spherical Coordinates
Slide 2
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Slide 3
Cartesian Coordinates
Cylindrical Coordinates
Spherical Coordinates
Cartesian Coordinates
Slide 4
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Cartesian: Differential Lengths
Slide 5
ˆxd dxa
Cartesian: Differential Lengths
Slide 6
ˆ ˆx yd dxa dya
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Cartesian: Differential Lengths
Slide 7
ˆ ˆ ˆx y zd dxa dya dza
Cartesian: Differential Areas
Slide 8
ˆxds dydza
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Cartesian: Differential Areas
Slide 9
ˆ ˆx yds dydza dxdza
Cartesian: Differential Areas
Slide 10
ˆ ˆ ˆx y zds dydza dxdza dxdya
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Cylindrical: Differential Lengths
Slide 13
ˆd d a
d
Cylindrical: Differential Lengths
Slide 14
ˆ ˆd d a d a
d
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Cylindrical: Differential Lengths
Slide 15
ˆ ˆ ˆzd d a d a dza
d
Cylindrical: Differential Areas
Slide 16
ˆds d dza
d
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Cylindrical: Differential Areas
Slide 17
ˆ ˆds d dza d dza
d
Cylindrical: Differential Areas
Slide 18
ˆ ˆ ˆzds d dza d dza d d a
d
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ˆrd dra
Spherical: Differential Lengths
Slide 21
ˆrdrard
dr
rd
sinr d
Spherical: Differential Lengths
Slide 22
ˆrdraˆsinr d a
ˆ
ˆsinrd dra
r d a
rd
dr
rd
sinr d
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Spherical: Differential Lengths
Slide 23
rd
dr
rd
ˆ
ˆ
ˆsin
rd dra
rd a
r d a
ˆrdra
ˆrd a
ˆsinr d a
sinr d
Spherical: Differential Areas
Slide 24
2 ˆsin rds r d d a
2 ˆsin rr d d a
dr
dr
rd
sinr d
rd
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Spherical: Differential Areas
Slide 25
2 ˆsin
ˆsinrds r d d a
r drd a
2 ˆsin rr d d a
ˆsinr drd a
dr
dr
rd
sinr d
rd
Spherical: Differential Areas
Slide 26
2 ˆsin
ˆsin
ˆ
rds r d d a
r drd a
rdrd a
2 ˆsin rr d d a
ˆsinr drd a
ˆrdrd a
dr
dr
rd
sinr d