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

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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