Electromagnetic Theory Engr.Mian Shahzad Iqbal Department of Telecom Engineering University of Engineering & Technology Taxila

Text Book Two textbooks will be used extensively throughout this course 1. Field and Wave Electromagnetic by David K.Chang 2. “Engineering Electromagnetic by William H.Hayt

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Field Vector Cartesian Coordinate System Orthonormal Unit Vectors Coordinates Limits Arbitrary Vector Field

Position Vector Cylindrical Coordinate System Orthonormal Unit Vectors Coordinates

Field Vector Spherical Coordinate System Orthonormal Unit Vectors Coordinates Arbitrary Vector Field Limits

Cartesian Coordinate System: Coordinate Surfaces, Unit Vectors, Surface Elements and Volume Element

Cylindrical Coordinate System: Coordinate Surfaces, Unit Vectors, Surface Elements and Volume Element

Spherical Coordinate System: Coordinate Surfaces, Unit Vectors, Surface Elements and Volume Element

Metric Coefficients and Vector Differential Line Elements Cartesian Coordinate System Cylindrical Coordinate System Spherical Coordinate System

Metric Coefficients and Differential Volume and Surface Elements Cartesian Coordinate System Cylindrical Coordinate System Spherical Coordinate System

Spherical CoordinatesCylindrical CoordinatesCartesian Coordinates Transformation Table Coordinates of Different Coordinate Systems

1.Formulate x as a function of the cylinder and spherical coordinates. 2.Formulate r as a function of the Cartesian and spherical coordinates. 3.Formulate as a function of the cylinder coordinates.. Examples

Cartesian CoordinatesCylindrical CoordinatesSpherical Coordinates Transformation Table Scalar Vector Components in Different Coordinate Systems

Electromagnetic  In EMT, we have to deal with quantities that depend on both time and position

Gradient  Gradient of a scalar field is a vector field which points in the direction of the greatest rate of increase of the scalar field, and whose magnitude is the greatest rate of change.

Gradient In the above two images, the scalar field is in black and white, black representing higher values, and its corresponding gradient is represented by blue arrows.

Divergence  Divergence is an operator that measures the magnitude of a vector field's source or sink at a given point  The divergence of a vector field is a (signed) scalar  For example, for a vector field that denotes the velocity of air expanding as it is heated, the divergence of the velocity field would have a positive value because the air expands. If the air cools and contracts, the divergence is negative. The divergence could be thought of as a measure of the change in density.

Curl  Curl is a vector operator that shows a vector field's "rotation";  The direction of the axis of rotation and the magnitude of the rotation. It can also be described as the circulation density.  "Rotation" and "circulation" are used here for properties of a vector function of position, regardless of their possible change in time.  A vector field which has zero curl everywhere is called irrotational.