Electromagnetic Theory | Co-ordinate Systems
Introduction to rectangular, cylindrical & spherical co-ordinate systems.
The co-ordinate systems are used to express and understand the concepts in electromagnetic theory. The physical quantities that we deal with in Electromagnetic theory are functions of space and time. To represent these spacial values we use anyone one of the co-ordinate systems. There are many co-ordinate systems but there are 3 which we can consider important for us. They are the rectangular co-ordinate system also called the cartesian co-ordinate system, the cylindrical co-ordinate system and the spherical co-ordinate system.
This might be the most familiar system of the three. The rectangular co-ordianate system uses 3 numerical values to represent the position of something in space. It has 3 axes named X,Y and Z and any point in space can be represent with these three numbers. These axes are also always perpendicular to each other. If you consider a vector A, it can be represented as (Ax,Ay,Az) which represents the distance of the vector point in each of the three directions.
The cylindrical co-ordinate system also represent the point using 3 values. The radius of the cylinder represented by the symbol ρ, the azimuthal angle which is measured from the X axis is represented by the symbol φ, and the distance along the Z axis. A vector A is represented as (Aρ, Aφ,Az) in this system.
The spherical co-ordinate system is similar to the cylindrical system. It uses the angle measured from the Z axis, called the colatitude represented by the symbol θ along with the radius and azimuthal angle as in the cylindrical system to represent the point in space. A vector A can be represented as (Aρ, Aθ, Aφ) in this system.
We can make relationships between the three different co-ordinate systems. The process of converting from one system to another is called co-ordinate transformation. The vector A can be transformed to the cylindrical co-ordinate system from rectangular co-ordinate system by the following matrix relation.
We can also transform the rectangular co-ordinate system to spherical by the martix relationship.
In short there are 3 main co-ordinate systems. These are very important in electromagnetic theory as they help to represent the values in space.
