محاضرة 2

¬¬¬¬¬¬¬1.1 Vector Representation
This introductory chapter is a review of mathematical concepts required for the electromagnetism. It is assumed that the reader is already familiar with elementary vector analysis.
Physical quantities that we deal with in electromagnetism can be scalars or vectors.
A scalar is an entity which only has a magnitude. Examples of scalars are mass, time, distance, electric charge, electric potential, energy, temperature etc. A vector is characterized by both magnitude and direction. Examples of vectors in physics are displacement, velocity, acceleration, force, electric ?eld, magnetic ?eld etc.
A vector is represented by a straight line of specific length having an arrow head which shows its direction. This straight line is called the representative line of that vector. Vector variables are sometimes notated with arrow above them (particularly in handwritten physics formulae), and sometimes notated by using a bold-face font (particularly in print).
A ?eld is a quantity which can be speci?ed everywhere in space as a function of position. The quantity that is speci?ed may be a scalar or a vector. For instance, we can specify the temperature at every point in a room. The room may, therefore, be said to be a region of “temperature ?eld” which is a scalar ?eld because the temperature T(x, y, z) is a scalar function of the position. An example of a scalar ?eld in electromagnetism is the electric potential.
In a similar manner, a vector quantity which can be speci?ed at every point in a region of space is a vector ?eld. For instance, every point on the earth may be considered to be in the gravitational force ?eld of the earth. We may specify the ?eld by the magnitude and the direction of acceleration due to gravity (i.e. force per unit mass) g(x, y, z) at every point in space. As another example consider ?ow of water in a pipe. At each point in the pipe, the water molecule has a velocity v ? (x, y, z). The water in the pipe may be said to be in a velocity ?eld. There are several examples of vector ?eld in electromagnetism, e.g., the electric ?eld E ?, the magnetic ?ux density B ? etc.