![]() ![]() The vector associated with a given point on the river’s surface gives the velocity of the water at that point. The larger object has greater mass, so it exerts a gravitational force of greater magnitude than the smaller object.įigure 6.2(b) shows the velocity of a river at points on its surface. The vectors of largest magnitude in the figure are the vectors closest to the larger object. At any point in the figure, the vector associated with a point gives the net gravitational force exerted by the two objects on an object of unit mass. How can we model the gravitational force exerted by multiple astronomical objects? How can we model the velocity of water particles on the surface of a river? Figure 6.2 gives visual representations of such phenomena.įigure 6.2(a) shows a gravitational field exerted by two astronomical objects, such as a star and a planet or a planet and a moon. In this section, we examine the basic definitions and graphs of vector fields so we can study them in more detail in the rest of this chapter. They are also useful for dealing with large-scale behavior such as atmospheric storms or deep-sea ocean currents. Vector fields are an important tool for describing many physical concepts, such as gravitation and electromagnetism, which affect the behavior of objects over a large region of a plane or of space. 6.1.3 Identify a conservative field and its associated potential function.6.1.2 Sketch a vector field from a given equation. ![]() ![]() 6.1.1 Recognize a vector field in a plane or in space. ![]()
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