Electromagnetic Fields: Fields and Coordinates

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ELECTROMAGNETIC FIELDS AND THEORY: FIELDS AND VECTORS: Fields and Coordinates

1.1 Fields.

We will understand by field a group of values that describe the magnitude of a physical phenomenon in a determined region. For example, a room’s temperature could be described using a field. The mentioned values could be continuous given by a mathematical function, or in a discrete way, using a listing.

In the case of a temperature, the field will be suffice by a number for each point, we will say that it’s a scalar field. If in the same room we would like to describe at a particular instant, the velocity of the air in each point, we would need three numbers for each point to be able to express the components of the velocity. We would then be referring to a vectorial field.

1.2 Coordinate Systems

The selection of the coordinate system in the resolution of an electromagnetism problem, is both very important and very easy.

It is necessary because problems that can be solved in a very easy way by choosing the proper coordinate system, may also be very difficult to solve using another one. To choose is easy because it is made according to the symmetry of the problem. For example, a problem related to a long cable, would require the use of a cylindrical coordinate system.

There are many existing coordinate systems, however, almost all of the problems can be formulated using the following three.