Vector Fields

Abstract

Picture a space, three-dimensional in the general case, throughout which, at every point, some physical characteristic has a definite magnitude and direction. Such a space with reference to the distribution of the vector representing such physical magnitude may be termed a “vector field”. Thus if we imagine an indefinite space, void except for a single sphere of matter at its center, then the distribution of gravity throughout such space will constitute a vector field. At every point the direction will lie toward the center of the sphere and the magnitude will vary inversely as the square of the distance from this center. At every point in such a space, therefore, there could be drawn a vector representing the force of gravity in direction and magnitude. If instead of one body there are two or more, the same general conditions will hold, but the field will be more complex in character. Nevertheless at each and every point the force of gravity will have a single definite value and a single definite direction, and will constitute a vector field.