Scalar function satisfying div f=F

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Discussion Overview

The discussion revolves around the process of finding a scalar function that satisfies the equation grad f = F, where F is a known vector field. The context includes mathematical reasoning and potential applications in physics, such as deriving electric potential from electric intensity.

Discussion Character

  • Technical explanation, Conceptual clarification, Homework-related

Main Points Raised

  • One participant initially inquires about an algorithm for finding a scalar function satisfying div f = F, indicating a misunderstanding of the divergence operation.
  • Another participant clarifies that divergence is not defined on scalars and points out that the divergence of a vector results in a scalar, prompting a re-evaluation of the original question.
  • A subsequent post corrects the initial inquiry to grad f = F and seeks to derive the scalar function f from the vector F, providing an example related to electric potential and electric intensity.
  • A link to an external resource is shared to illustrate the concept further.
  • A later reply expresses gratitude, indicating that the provided information was helpful.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the initial misunderstanding regarding divergence, but there is agreement on the corrected formulation involving the gradient. The discussion remains focused on the process of deriving scalar functions from vector fields.

Contextual Notes

The discussion reflects some confusion regarding the definitions and operations involving scalar and vector fields, particularly in the context of divergence and gradient. There may be assumptions about the familiarity with these concepts that are not explicitly stated.

rammer
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What's the algorithm for finding scalar function satisfying div f=F if I know vector F?
 
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There isn't one. div is not defined on scalars and the divergence of a vector would be a scalar. What did you really mean to ask?
 
Sorry, I meant grad f=F, and I want to get scalar function f from vector F (for instance electric potential from electric intensity).
 
rammer said:
Sorry, I meant grad f=F, and I want to get scalar function f from vector F (for instance electric potential from electric intensity).

Look at the following link for an example:

http://www.math.wisc.edu/~conrad/f07/potentials.pdf
 
thanks, that's exactly what i was looking for
 

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