- #1
MathematicalPhysics
- 40
- 0
I want to find which values of n make the vector field
[tex]\underline{F} = {|\underline{r}|}^n\underline{r}[/tex] solenoidal.
So I have to evaluate the divergence of this vector field I think, then show for which values of n it is zero?
Im starting by substituting:
[tex]\underline{r} = \sqrt{x^2 + y^2 + z^2}[/tex]
getting..
[tex] \underline{F} = {(x^2 + y^2 + z^2)}^{n/2}\sqrt{x^2 + y^2 + z^2}[/tex]
How can I extract
[tex]\underline{F_x}, \underline{F_y}, \underline{F_z}[/tex]?
It's probably really simple but I can't see it! Thanks in advance.
[tex]\underline{F} = {|\underline{r}|}^n\underline{r}[/tex] solenoidal.
So I have to evaluate the divergence of this vector field I think, then show for which values of n it is zero?
Im starting by substituting:
[tex]\underline{r} = \sqrt{x^2 + y^2 + z^2}[/tex]
getting..
[tex] \underline{F} = {(x^2 + y^2 + z^2)}^{n/2}\sqrt{x^2 + y^2 + z^2}[/tex]
How can I extract
[tex]\underline{F_x}, \underline{F_y}, \underline{F_z}[/tex]?
It's probably really simple but I can't see it! Thanks in advance.