from one coordinate system to other
Subject and UNIT: Electromagnetic Theory: Unit I: (a) Vector Analysis
• Getting familiar with the dot product and cross product, it is possible now to transform the vectors from one co-ordinate system to other co-ordinate system.
scalar, vector triple product
Subject and UNIT: Electromagnetic Theory: Unit I: (a) Vector Analysis
Then the product of these three vectors is classified in two ways called, 1. Scalar triple product 2. Vector triple product
Properties, Applications, Solved Example Problems
Subject and UNIT: Electromagnetic Theory: Unit I: (a) Vector Analysis
Vector or Cross Product of Vectors
Properties, Applications, Solved Example Problems
Subject and UNIT: Electromagnetic Theory: Unit I: (a) Vector Analysis
The result of such a dot product is scalar hence it is also called scalar product.
Subject and UNIT: Electromagnetic Theory: Unit I: (a) Vector Analysis
Let us discuss the multiplication of two or more vectors. The knowledge of vector multiplication allows us to transform the vectors from one coordinate system to other.
represent field vectors, Solved Example Problems
Subject and UNIT: Electromagnetic Theory: Unit I: (a) Vector Analysis
• The surfaces which are used to define the spherical co-ordinate system on the three cartesian axes are,
represent field vectors, Solved Example Problems
Subject and UNIT: Electromagnetic Theory: Unit I: (a) Vector Analysis
• The circular cylindrical co-ordinate system is the three dimensional version of polar co-ordinate system. The surfaces used to define the cylindrical co-ordinate system are,
represent field vectors, Solved Example Problems
Subject and UNIT: Electromagnetic Theory: Unit I: (a) Vector Analysis
• This is also called rectangular co-ordinate system. This system has three co-ordinate axes represented as x, y and z which are mutually at right angles to each other. These three axes intersect at a common point called origin of the system. There are two types of such system called 1. Right handed system and 2. Left handed system.
Vector Analysis
Subject and UNIT: Electromagnetic Theory: Unit I: (a) Vector Analysis
• To describe a vector accurately and to express a vector in terms of its components, it is necessary to have some reference directions.
Scaling, Addition, Subtraction
Subject and UNIT: Electromagnetic Theory: Unit I: (a) Vector Analysis
• The various mathematical operations such as addition, subtraction, multiplication etc. can be performed with the vectors. In this section the following mathematical operations with the vectors are discussed.
Subject and UNIT: Electromagnetic Theory: Unit I: (a) Vector Analysis
• In two dimensions, a vector can be represented by a straight line with an arrow in a plane.
Definition, Example
Subject and UNIT: Electromagnetic Theory: Unit I: (a) Vector Analysis
• The various quantities involved in the study of engineering electromagnetics can be classified as, 1. Scalars and 2. Vectors