Find the unit normal of a solid ball of radius $r$ centred at the origin in $\mathbb{R}^3$

Question

How would I find the unit normal $n(x)$ of a solid ball of radius $r$ centered at $(0,0,0)$, that points out of the the solid ball at $x$?

Answer 1

For a ball of radius $R > 0$ centered at $x_{0}$ in $\mathbf{R}^{N}$, the unit normal at a boundary point $x$, a.k.a., the unique unit vector at $x$ that points directly away from the center, is $$ n(x) = \frac{x - x_{0}}{R}. $$