A First Course in Mathematical Physics by Whelan Colm T.;

Author:Whelan, Colm T.;
Language: eng
Format: epub
Publisher: John Wiley & Sons, Incorporated
Published: 2016-01-26T00:00:00+00:00

to write

7.58

We have found the required decomposition, with

7.59

However, we can go further and write both and terms in a more revealing form. Now

7.60

but

Hence

7.61

We can now apply the divergence theorem to the first term on the right to get

7.62

For the vector term, we have

7.63

where we have made use of Problem 6.13. Our vector field, remains bounded as , so assuming that is very large, the surface integrals both go to zero and we may write

7.64

where

7.65

where is all space.

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