Flux Equations for a Solid Surface and a Curve

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SUMMARY

The discussion confirms that one equation represents a flux integral over a solid surface in three dimensions, while the other represents a flux integral over a curve in two dimensions. The first equation explicitly mentions "surface," indicating it is a surface integral, whereas the second equation uses "ds" instead of "dS," suggesting it is a path integral. The distinction between these two types of integrals is crucial for understanding the flow of a vector field across different geometrical entities.

PREREQUISITES
  • Understanding of vector calculus, specifically surface and line integrals.
  • Familiarity with the concepts of flux and its mathematical representation.
  • Knowledge of three-dimensional and two-dimensional geometrical interpretations.
  • Basic proficiency in interpreting mathematical notation related to integrals.
NEXT STEPS
  • Study the properties of surface integrals in vector calculus.
  • Learn about line integrals and their applications in physics.
  • Explore the Divergence Theorem and Stokes' Theorem for deeper insights into flux.
  • Review examples of flux calculations in both three-dimensional and two-dimensional contexts.
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Students and professionals in mathematics, physics, and engineering who are dealing with vector fields and integrals, particularly those focusing on fluid dynamics and electromagnetism.

Miike012
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are both of the equations i posted flux equations. one of them is for a surface of a solid and the other is for a curve?
 

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If you meant "Is one of them is for a surface of a solid and the other is for a curve?", yes, the first specifically says "surface" and the second, while you have only given the form, has "ds" rather than "dS" and so is a path integral.

Also, the first is for flux across (through) the surface in 3 dimensions while the second is for flux across the closed path, in 2 dimensions, and so the flow in and out of the region bounded by that closed path.
 
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well the first one is definitely a surface integral because the question says so. The second one is less obvious. The fact that there is only one integral sign might imply that the integral is over a curve...

Is this for a larger homework question? Maybe you can tell which it is meant to be from what the rest of the question says.
 

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