electromagnetic theory (te-232) -...

Electromagnetic Theory (TE-232)

Lecture by:Mr. Shakir Karim Buksh

Assistant ProfessorTelecommunication Engineering Department

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Vector Calculus

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Lecture 4

By: Shakir Karim BukshTelecommunication Engineering Department

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Differential Length, Area & Volume

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Differential Elements in length, area & volume

are useful in Vector Calculus.

We are defining them for

•Cartesian Coordinate System

•Circular Cylindrical System

•Spherical System

Cartesian Coordinate System

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Cartesian Coordinate System (contd/2)

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Cartesian Coordinate System (contd/3)

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Cylindrical Coordinate System

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Cylindrical Coordinate System (contd/2)

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Cylindrical Coordinate System (contd/3)

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Cylindrical Coordinate System (contd/3)

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Cylindrical Coordinate System (contd/3)

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Cylindrical Coordinate System (contd/4)

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Cylindrical Coordinate System (contd/4)

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Cylindrical Coordinate System (contd/4)

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Cylindrical Coordinate System (contd/4)

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Cylindrical Coordinate System (contd/4)

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Cylindrical Coordinate System (contd/4)

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Cylindrical Coordinate System (contd/4)

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Cylindrical Coordinate System (contd/4)

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Cylindrical Coordinate System (contd/4)

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Cylindrical Coordinate System (contd/4)

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Spherical Coordinate System

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Spherical Coordinate System

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Spherical Coordinate System

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Spherical Coordinate System (contd/2)

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Spherical Coordinate System (contd/2)

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Differential Length, Surface Area and Volume elements for each geometry

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Line, Surface & Volume Integrals

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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.

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Line, Surface & Volume Integrals

By: Shakir Karim BukshTelecommunication Engineering Department

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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)

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Line, Surface & Volume Integrals

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Line, Surface & Volume Integrals

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Line, Surface & Volume Integrals

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NOTE:

a closed path defines an open surface as shown in Figure 3.11

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Line, Surface & Volume Integrals

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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

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Line, Surface & Volume Integrals

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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

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Line, Surface & Volume Integrals

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The Next Lecture will be on

differentiation of Vectors

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