Scalars and Vectors

 Scalars and Vectors

• The various quantities involved in the study of engineering electromagnetics can be classified as,

1. Scalars and 2. Vectors

1. Scalar

• The scalar is a quantity whose value may be represented by a single real number, which may be positive or negative. The direction is not at all required in describing a scalar. Thus,

• A scalar is a quantity which is wholly characterized by its magnitude.

• The various examples of scalar quantity are temperature, mass, volume, density, speed, electric charge etc.

2. Vector

• A quantity which has both, a magnitude and a specific direction in space is called a vector. In electromagnetics vectors defined in two and three dimensional spaces are required but vectors may be defined in n-dimensional space. Thus,

• A vector is a quantity which is characterized by both, a magnitude and a direction.

• The various examples of vector quantity are force, velocity, displacement, electric field intensity, magnetic field intensity, acceleration etc.

3. Scalar Field

• A field is a region in which a particular physical function has a value at each and every point in that region. The distribution of a scalar quantity with a definite position in a space is called scalar field. For example the temperature of atmosphere. It has a definite value in the atmosphere but no need of direction to specify it hence it is a scalar field. The height of surface of earth above sea level is a scalar field. Few other examples of scalar field are sound intensity in an auditorium, light intensity in a room, atmospheric pressure in a given region etc.

4. Vector Field

• If a quantity which is specified in a region to define a field is a vector then the corresponding field is called a vector field. For example the gravitational force on a mass in a space is a 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, wind velocity of atmosphere, voltage gradient in a cable, displacement of a flying bird in a space, magnetic field existing from north to south field etc.

Review Question

1. Discuss the scalar and vector fields with examples.