Can someone please help as I am stuck,
I need to show that
$$\phi=\frac{k}{2\pi}\log(x^{2}+y^{2})^{1/2}$$
satisfies Laplaces equation, however I cannot seem to differentiate this function. Note $k$ is a constant.
How do I go about partially differentiating
$$\log(\sqrt{x^{2}+y^{2}})$$
I was thinking, using chain rule, just call
$$\sqrt{x^{2}+y^{2}}=r$$
so $$\frac{1}{r}\log r+\log r$$
Any help is appreciated.
Best Answer
I would think that you would immediately use $log(\sqrt{x^2+ y^2})= \frac{1}{2}log(x^2+ y^2)$. That will simplify your problem.