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The Scalar Potential Field

In: An Introduction to Vector Analysis For Physicists and Engineers

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  • B. Hague

Abstract

Let S be a scalar point-function which may be mapped out in space by a series of level surfaces, upon each of which the scalar has a definite but different constant value. These surfaces divide up the region of space into a series of layers or laminae. Associated therewith is a vector field Vs directed everywhere normal to the level surfaces, i.e. in the direction of the greatest rate of increase of S at any point and having a magnitude equal to that rate of increase. This is expressed by 4.3, namely, $$ {V_s} = gradS = \nabla S. $$

Suggested Citation

  • B. Hague, 1970. "The Scalar Potential Field," Springer Books, in: An Introduction to Vector Analysis For Physicists and Engineers, chapter 6, pages 91-100, Springer.
    • Handle: RePEc:spr:sprchp:978-94-009-5841-8_6
    DOI: 10.1007/978-94-009-5841-8_6
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