Definition of Potential

The problem of generating a vector field from the gradient of a scalar function is illustrated in electrostatics. Here, the scalar function f(r) --> the electrostatic potential V(r). The vector field grad f --> the electrostatic field E =
-grad V.

(7)

Problems of this type appear frequently in other areas of physics and engineering; for example, in heat transfer.

In Equation (7), the position vector r can be expressed in the rectangular coordinates (x, y, z), spherical coordinates (<EM>r</EM>, <EM>theta</EM>, <EM>phi</EM>), or cylindrical coordinates (<EM>r</EM>,<EM>theta</EM>, <EM>z</EM>), the choice being made by the geometry of the problem. Similarly, the gradient operator grad is to be expressed in terms of the chosen coordinates.

For a detailed discussion of the Gradient, refer to the Project Links Gradient Module

Now go on to answer some questions about what you just learned. You may also wish to examine some applications of these topics.


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