# Charge density for V=x^2-y^2+Z^2

1. Sep 3, 2009

### 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 .

2. Sep 3, 2009

### gabbagabbahey

Hint:What does Poisson's Equation tell you?

3. Sep 4, 2009

### 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?

4. Sep 4, 2009

### kuruman

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

5. Sep 4, 2009

### 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 ?

6. Sep 4, 2009

### 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.