Normal derivative is defined as:(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \frac{\partial u}{\partial n} = \nabla u \;\cdot\; \hat{n} [/tex]

Where [itex]\hat{n}[/itex] is the unit outward normal of the surface of the sphere and for a small sphere with surface [itex]\Gamma[/itex], the book gave:

[tex]\int_{\Gamma} \frac{\partial u}{\partial n} \;dS \;=\; -\int_{\Gamma} \frac{\partial u}{\partial r} \;dS [/tex]

The book claimed on a sphere:

[tex] \frac{\partial u}{\partial n} = \nabla u \;\cdot\; \hat{n} \;=\; -\frac{\partial u}{\partial r} [/tex]

Where [itex]r [/itex] is the radius of the sphere. I understand [itex]\hat{n}[/itex] is parallel to [itex]\vec{r}[/itex] but [itex]r[/itex] is not unit length.

Can anyone help?

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Normal derivative in a sphere.

Loading...

Similar Threads - Normal derivative sphere | Date |
---|---|

Imposing normalization in numerical solution of of ODE | Apr 17, 2015 |

Normalizing boundary conditions | Nov 21, 2014 |

Normal derivative at boundary Laplace's equation half plane | May 1, 2014 |

Derivation of normal surface vector of a quasilinear PDE | Apr 9, 2012 |

Normal derivative of Green's function on a disk. | Aug 23, 2010 |

**Physics Forums - The Fusion of Science and Community**