dot or scalar product of two unit vectors

Last time I have written about the properties of unit vectors that is:

Dot product of unit vectors :

i.i=1

j.j=1

k.k=1

i.j=j.k=k.i=0

Do you know how the above results come? If your answer is no, then let us discuss it:

I have already explained in my earlier articles that dot product or scalar product between two vectors A and B is given as:

A.B = AB cos θ

where θ is the angle between A and B. A and B are magnitudes of A and B.

As i the unit vector along x axis Continue reading “dot or scalar product of two unit vectors”

Coordinate systems

Coordinate system is used to represent any point, say P(x, y, z ) in space. There are many methods by which this can be done, but there  are three simple methods, which we will discuss in this article.

Types of coordinate systems are :

I. Cartesian or rectangular coordinate system.

II  Cylindrical coordinate system

III Spherical coordinate system.

Today I will discuss briefly about the cartesian or rectangular coordinate system:

Unit vector, vector dot product, vector cross product, triple cross product, scalar triple product

Unit Vector. Any vector A can be represented by the magnitude of the vector |A| multiplied by its unit vector written as an

So A = |A| an.

A unit vector has the direction of the main vector is of unit magnitude. It is the ratio of vector itself by its magnitude.

Thus,the magnitude of a unit vector is one.

Scalar or Dot Product of Two Vectors:

Scalar and vector analysis

Let us discuss today about two quantities called scalars and vectors. Suppose you are going in your car or bike. Your vehicle must have speedometer which shows the speed. Let the speed is 60 km/hour. Now suppose you have certain instrument which shows that you are going in north direction with 60 km/hour.

So the 60 km/hr means only the magnitude or value. So the quantities which have only magnitudes or values are called scalars.

But the 60 km/hr in north direction means the quantity has value as well as direction in it. These quantities are called vector quantities.

Therefore the more technical definitions will be: Continue reading “Scalar and vector analysis”

Applications of electromagnetic field theory

Electromagnetic Field Theory has applications in analysing and designing of communication system like:

Difference between circuit theory and electromagnetic field theory

Circuit Theory: As the name suggests, circuit theory deals with electrical circuit. An engineer can predict the performance of complicated electrical networks with the help of circuit theory. But this theory has certain limitations like :

• It cannot be applied in free space.
• It is useful only at low frequencies.

This theory is unsuccessful in explaining the radiation of electromagnetic waves into space in radio communications.

It cannot be used to analyse or design a complete communication system. Example: Radio Communication System.

Electromagnetic Field Theory. Although electromagnetic Field Theory (EMFT) is complex in comparison with circuit theory but EMFT is simplified by using appropriate mathematics. This theory deals with E and H vectors, whereas circuit theory deals with voltages and currents.
This theory has following advantages in comparison to circuit theory:

• It is also applicable in free space.
• It is useful at all frequencies, particularly at high frequencies,
• The radiation effect can be considered.
• This theory can be used to analyse or design a complete communication system. Example: Wireless Communication, Radio Communication.

Thus above are the difference between circuit theory and electromagnetic field theory.