Hi,(adsbygoogle = window.adsbygoogle || []).push({});

I am trying to chew through the proof of reciprocity in MRI. At some point I come across to the following expression:

[itex]\Phi_{M}[/itex]=[itex]\oint\vec{dl}[/itex][itex]\cdot[/itex][itex]\left[\frac{\mu_{0}}{4\pi}\int{d^{3}r'}\frac{\vec{\nabla'}\times\vec{M}(\vec{r'})}{\left|\vec{r}-\vec{r'}\right|}\right][/itex]

Now it says that by using integration by parts (where surface term can be ignored for finite current sources), and using vector identity, [itex]\vec{A}\cdot\left(\vec{B}\times\vec{C}\right)=-\left(\vec{A}\times\vec{C}\right)\cdot\vec{B}[/itex], we get

[itex]\Phi_{M}=\frac{\mu_{0}}{4\pi}\int{d^{3}r'\vec{M}(\vec{r'})\cdot\left[\vec{\nabla'}\times\left(\oint\frac{\vec{dl}}{\left|\vec{r}-\vec{r'}\right|}\right)\right]}[/itex]

Can someone explain to me how to use integration by parts in this case and what does ignoring surface term mean in this context?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

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

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

# Integration by parts problem involving vector functions

Loading...

Similar Threads for Integration parts problem |
---|

I How to derive this log related integration formula? |

I An integration Solution |

B I Feel Weird Using Integral Tables |

I Integration by parts |

A Integration by parts of a differential |

**Physics Forums | Science Articles, Homework Help, Discussion**