Objective: Define vector field
Introduction
Vector fields are used to describe physical phenomena such as gravitation, electromagnetism, atmospheric storms and deep-sea ocean currents. Let's give some examples.
Example (a). Gravitational force exerted by two astronomical objects such as a planet and a star or a planet and its moon.
The figure (a) models the gravitational force exerted by these two objects:
At any point in the figure, a vector associated with that point gives the net gravitational force exerted by the two objects on a unit of mass of an object. The vectors of the greater magnitude are associated with the largest object. The greater the mass of an object, the stronger is its gravitational force. The gravitational force of the larger object is stronger than that of the smaller object. The vectors of smaller magnitude are associated with the smaller object. The mass of this object is smaller. Its gravitational force is less strong than the larger object.
Example (b). Velocity of a river at points on its surface.
The vector field velocity of water on a river shows the varied speeds of water. Vectors in red are of greater magnitude. Therefore, the water flows quickly. Vectors in blue are smaller in magnitude. They show a smaller flow of water.
As we can see in these two examples, a vector field is a map of vectors. In the following posts we will study vectors fields in R² and R³.
Definition
Example
Solution
Practice
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