Mehran University of Engineering & Technology SZAB khairpur campus Made by: Noshad soomro k-12EL70

Topics Vector field Scalar field Vector Analysis

Vector Analysis Vector analysis is a mathematical tool with which electromagnetic (EM) concepts are most conveniently expressed. A quantity is called a scalar if it has only magnitude examples: mass, temperature, electric potential A quantity is called a vector if it has both magnitude and direction examples: velocity, force, electric field intensity).

When two vectors A and B are multiplied, the result is either a scalar or a vector depending on how they are multiplied. There are two types of vector multiplication: 1. Scalar (or dot) product: (A.B) 2.Vector (or cross) product: (AxB) 1.The dot product of the two vectors A and B is defined geometrically as the product of the magnitude of B and the projection of A onto B (or vice versa): where theta is the smaller angle between A and B

The cross product of two vectors A and B is defined as Field: A field can be defined as a function that specifies a particular quantity everywhere in a region or describing a quantity at all points in space

scalar fields: If at every point in a region, a scalar function has a defined value, the region is called a scalar field. or The distribution of a scalar quantity with a definite position in a space is called scalar field Example: the temprature of atmosphere, it has a definite value in the atmosphere but no need of direction to specify it, hence it is a scalar field. or The height of surface of earth above sea level is a scalar field.

A scalar field such as temperature or pressure, where intensity of the field is graphically represented by different hues of color.

Vector field If at every point in a region, a vector function has a defined value, the region is called a vector field. Or If a quantity which is specified in a region to define a field is a vector then the corresponding field is called vector field. Example: the gravitational force on a mass in a space is vector field. This force has a value at various points in a space and always has a specific direction. The other examples of vector field are the velocity of particles in a moving fluid and magnetic field existing from north to south field etc

for example, the speed and direction of a moving fluid throughout space, or the strength and direction of some force, such as the magnetic or gravitational force, as it changes from point to point