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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.





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