Is the Potential V=x^2-y^2+z^2 Valid in Free Space?

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Homework Help Overview

The discussion revolves around the validity of the potential distribution equation V = x² - y² + z² in free space, particularly in relation to its compliance with Laplace's and Poisson's equations.

Discussion Character

  • Conceptual clarification, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore whether the given potential satisfies the conditions of free space, referencing Laplace's and Poisson's equations. Questions arise regarding the implications of the potential's dimensional correctness and its relation to charge density.

Discussion Status

The discussion is active, with participants providing hints and exploring the implications of the potential's validity. Some guidance has been offered regarding the use of Poisson's equation, while multiple interpretations of the potential's correctness and its consequences are being examined.

Contextual Notes

There is an ongoing debate about the dimensional correctness of the potential equation and its implications for calculating charge density. The participants are navigating the constraints of the problem without reaching a consensus.

knavneet
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Can anyone tell me if the potential distribution equations V= x2-Y2+Z2
holds in free space, if not, please help me to find the charge density from the given potential .
 
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Hint:What does Poisson's Equation tell you?
 
Del2V=2 for the given V, so the given potential doesn't satisfy Laplace equation, So i think this potential is not possible in free space. But how to calculate charge density then?
 
Yes, Laplace's equation is not valid. However Poisson's equation is. As gabbagabbahey said, What does Poisson's equation tell you?
 
According to Poisson equation Del2V=-charge density / epslion ,
But in our problem Del2V=2 , So charge density = 2*epsilon , Is it the answer now ?
 
On the basis of what you have said, no. The equation, V= x2-y2+z2 is dimensionally incorrect. Therefore any answer derived from it cannot be correct.
 

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