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

[knavneet]

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 .

 

[gabbagabbahey]

Hint:What does Poisson's Equation tell you?

 

[knavneet]

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?

 

[kuruman]

Yes, Laplace's equation is not valid. However Poisson's equation is. As gabbagabbahey said, What does Poisson's equation tell you?

 

[knavneet]

According to Poisson equation Del²V=-charge density / epslion ,
But in our problem Del²V=2 , So charge density = 2*epsilon , Is it the answer now ?

 

[kuruman]

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.