Timeline for Charge density definition in Cylindrical Coordinates
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 16, 2018 at 19:56 | comment | added | JoeSwap | The factor of $2\pi$ comes from the dirac distribution naturally: fen.bilkent.edu.tr/~ercelebi/mp03.pdf | |
| Jan 24, 2018 at 18:45 | vote | accept | JoeSwap | ||
| Jan 24, 2018 at 18:44 | comment | added | secavara | The integration argument is fundamental to me, in the sense that the least that we could demand is that $Q = \int \rho \, dV$. There are not many alternatives... something like $\delta(\phi)$ which in principle could work for $Q$ is something I've never seen (given the fact that the $z$ axis is a sick region for the angular coordinate) whereas you find this $2 \pi$ in, for instance, eq. 3.132 of Jackson's book, Classical Electrodynamics. | |
| Jan 24, 2018 at 18:31 | comment | added | JoeSwap | Thanks @secavara. The heaviside modification makes a lot of sense (I was not thinking about z being negative which needs to be included as well!). I still do not understand the $2\pi$ factor. I know we need it to get the total charge but what is the (previous to integration) reason? Is it related with the delta dirac in cylindrical coordinates? | |
| Jan 24, 2018 at 18:27 | history | edited | secavara | CC BY-SA 3.0 |
added 40 characters in body
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| Jan 24, 2018 at 18:21 | history | answered | secavara | CC BY-SA 3.0 |