| The phenomenons of electromagnetic field and wave have complex space-time distribution. To describe the characteristic of electromagnetic field, it is important to show various visualization figure of their variety based on space-time distribution. In general, the calculation of the electromagnetic field is very difficult because it is related with many mathematic operations. At the same, it is difficult to solve complex electromagnetic problem by means of manual calculation, and it is apparently deficient to get only simplistic or indirect physical figure to explain complex electromagnetic phenomenons. Although we can find many electromagnetic field figures in many monographs and papers, but we usually couldn't know how to get it and how to simulate with computer, therefore, it is necessary to use Mathematica to solve complex electromagnetic problem and its visualization rapidly.In this paper, the basic operation and expression characteristic of Mathematica is introduced systematically, then this paper deals with electromagnetic problem by using some of specific examples in calculation and visualization by means of Mathematica. Some charge distribution problems are discussed and visualization figures about some static electric field are obtained. The application of Mathematica in static magnetic field is discussed and the distribution figure of static magnetic field is showed.The propagation of electromagnetic wave is discussed and its figure about space-time distribution is given. The radiation of electromagnetic wave is discussed and compared with the results which have already been known. As a result, making use of the functions and software packages of Mathematica,it shows vast application prospect in electromagnetic calculation and its visualization easily.
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