Solution
= Solution
The radial <Laplace equation> has solution $a+b/r$. Boundedness at the origin requires $b=0$, and the value at $r=1$ fixes $a=1$. Thus
$$
\boxed{\psi(r)=1,\qquad0\le r\le1.}
$$
= Solution
The radial <Laplace equation> has solution $a+b/r$. Boundedness at the origin requires $b=0$, and the value at $r=1$ fixes $a=1$. Thus
$$
\boxed{\psi(r)=1,\qquad0\le r\le1.}
$$