require(bigints)The surface charge density induced on the metal surface of the cathode pad plane, by a charge \(q\) at a distance \(x_0\) from the pad plane, is given by:
\[\sigma (y,z) = \epsilon_0 E_x(y,z)\]
\[where\]
\[E_x(y,z)=- \frac{qx_0}{2\pi\epsilon_0(x_0^2+y^2+z^2)^\frac{2}{3}}\] \[and\]
\[E_z=E_y=0\]
Integrating this charge density over the metal surface, gives the total charge \(Q\) induced on the cathode pad plane, as follows:
\[Q=\int_{-\infty}^\infty\int_{-\infty}^\infty\sigma(y,z)dydz = -q\]
Using this approach of integration over each pad
## [1] "Removed 72305 entries"events <- sapply(j,`[[`,"Event")
events <- as.numeric(events)
tracks <- sapply(j, `[[`,"track")
tracks <- as.numeric(tracks)
v0s <- sapply(j, `[[`,"V0TrackID")
v0s <- as.numeric(v0s)
pdg <- sapply(j, `[[`,"pdgCode")
pdg <- as.numeric(pdg)detectors <- sapply(j, `[[`,"det0")
columns <- sapply(j, `[[`,"col0")
rows <- sapply(j,`[[`,"row0")
pads <- sapply(j,`[[`,"layer0")look.up.table <- data.frame(cbind(events,tracks,v0s,pdg))
look.up.table$index <- 1:nrow(look.up.table)require(dplyr)
look.up.table <- look.up.table %>%
mutate(unique.id=paste0(events,"-",tracks)) %>%
group_by(unique.id) %>%
mutate(n=n()) %>%
arrange(desc(n))require(knitr)
kable(head(look.up.table,100))| events | tracks | v0s | pdg | index | unique.id | n |
|---|---|---|---|---|---|---|
| 22000 | 0 | 4 | 211 | 64933 | 22000-0 | 10 |
| 22000 | 0 | -35 | -211 | 100964 | 22000-0 | 10 |
| 22000 | 0 | -35 | -211 | 140125 | 22000-0 | 10 |
| 22000 | 0 | -15 | -211 | 146038 | 22000-0 | 10 |
| 22000 | 0 | -8 | -211 | 327736 | 22000-0 | 10 |
| 22000 | 0 | -55 | -211 | 387895 | 22000-0 | 10 |
| 22000 | 0 | 4 | 211 | 430694 | 22000-0 | 10 |
| 22000 | 0 | -14 | 11 | 514908 | 22000-0 | 10 |
| 22000 | 0 | -32 | -211 | 627609 | 22000-0 | 10 |
| 22000 | 0 | -25 | -211 | 680298 | 22000-0 | 10 |
| 11669 | 2 | 46 | 211 | 32602 | 11669-2 | 9 |
| 11669 | 2 | 50 | 211 | 35518 | 11669-2 | 9 |
| 29444 | 0 | 17 | 211 | 171661 | 29444-0 | 9 |
| 29444 | 0 | 25 | 211 | 191788 | 29444-0 | 9 |
| 29444 | 0 | 7 | 211 | 237843 | 29444-0 | 9 |
| 11669 | 2 | 11 | 211 | 342498 | 11669-2 | 9 |
| 29444 | 0 | -19 | -211 | 400717 | 29444-0 | 9 |
| 11669 | 2 | -13 | -211 | 434010 | 11669-2 | 9 |
| 29444 | 0 | 5 | 211 | 439252 | 29444-0 | 9 |
| 29444 | 0 | 4 | 211 | 446430 | 29444-0 | 9 |
| 11669 | 2 | 103 | 211 | 471207 | 11669-2 | 9 |
| 29444 | 0 | -12 | -211 | 536327 | 29444-0 | 9 |
| 11669 | 2 | 7 | 211 | 574877 | 11669-2 | 9 |
| 11669 | 2 | -23 | -211 | 606696 | 11669-2 | 9 |
| 29444 | 0 | 19 | 211 | 625602 | 29444-0 | 9 |
| 11669 | 2 | -38 | -211 | 658774 | 11669-2 | 9 |
| 29444 | 0 | -27 | -211 | 700306 | 29444-0 | 9 |
| 11669 | 2 | -23 | -211 | 714978 | 11669-2 | 9 |
| 17148 | 0 | 6 | 211 | 4105 | 17148-0 | 8 |
| 26644 | 2 | -4 | 11 | 12132 | 26644-2 | 8 |
| 28273 | 5 | -34 | -211 | 38694 | 28273-5 | 8 |
| 26644 | 2 | 42 | 211 | 45028 | 26644-2 | 8 |
| 27630 | 2 | 100 | 211 | 48172 | 27630-2 | 8 |
| 19427 | 0 | -282 | -211 | 51193 | 19427-0 | 8 |
| 17148 | 0 | -73 | -211 | 64890 | 17148-0 | 8 |
| 28273 | 5 | -23 | -211 | 76524 | 28273-5 | 8 |
| 15154 | 1 | 24 | 211 | 79755 | 15154-1 | 8 |
| 33862 | 3 | 4 | 211 | 81426 | 33862-3 | 8 |
| 29214 | 0 | 17 | -11 | 88168 | 29214-0 | 8 |
| 19427 | 0 | 12 | 211 | 95812 | 19427-0 | 8 |
| 467 | 1 | 17 | 211 | 100744 | 467-1 | 8 |
| 27630 | 2 | 42 | -11 | 101015 | 27630-2 | 8 |
| 27630 | 2 | 32 | 211 | 109912 | 27630-2 | 8 |
| 467 | 1 | 38 | 211 | 132771 | 467-1 | 8 |
| 467 | 1 | 17 | 211 | 139907 | 467-1 | 8 |
| 27630 | 2 | 42 | -11 | 140175 | 27630-2 | 8 |
| 28273 | 5 | -57 | 11 | 141363 | 28273-5 | 8 |
| 467 | 1 | 1 | 211 | 149268 | 467-1 | 8 |
| 15154 | 1 | 19 | 211 | 149425 | 15154-1 | 8 |
| 27630 | 2 | -27 | -211 | 150842 | 27630-2 | 8 |
| 31005 | 1 | 5 | 211 | 165670 | 31005-1 | 8 |
| 33862 | 3 | 16 | 211 | 171710 | 33862-3 | 8 |
| 33862 | 3 | 142 | -11 | 172094 | 33862-3 | 8 |
| 19427 | 0 | -12 | -211 | 173264 | 19427-0 | 8 |
| 29214 | 0 | -50 | -211 | 174475 | 29214-0 | 8 |
| 31005 | 1 | 5 | 211 | 179056 | 31005-1 | 8 |
| 28273 | 5 | -21 | -211 | 188537 | 28273-5 | 8 |
| 27630 | 2 | 45 | 211 | 206259 | 27630-2 | 8 |
| 15154 | 1 | 8 | 211 | 219784 | 15154-1 | 8 |
| 15154 | 1 | 8 | 211 | 230117 | 15154-1 | 8 |
| 29214 | 0 | 46 | 211 | 244912 | 29214-0 | 8 |
| 42684 | 1 | -5 | -211 | 261993 | 42684-1 | 8 |
| 26644 | 2 | -42 | -211 | 273799 | 26644-2 | 8 |
| 31005 | 1 | 66 | -11 | 275519 | 31005-1 | 8 |
| 33862 | 3 | 179 | 211 | 302912 | 33862-3 | 8 |
| 42684 | 1 | 114 | 211 | 315214 | 42684-1 | 8 |
| 27630 | 2 | -49 | -211 | 315518 | 27630-2 | 8 |
| 28273 | 5 | 67 | 211 | 325192 | 28273-5 | 8 |
| 27630 | 2 | 20 | 211 | 336117 | 27630-2 | 8 |
| 17148 | 0 | 23 | 211 | 351355 | 17148-0 | 8 |
| 26644 | 2 | -30 | 11 | 360903 | 26644-2 | 8 |
| 28273 | 5 | 33 | 211 | 363040 | 28273-5 | 8 |
| 28273 | 5 | 12 | 211 | 379137 | 28273-5 | 8 |
| 31005 | 1 | 19 | 211 | 383600 | 31005-1 | 8 |
| 31005 | 1 | -76 | -211 | 388396 | 31005-1 | 8 |
| 17148 | 0 | 36 | 211 | 409334 | 17148-0 | 8 |
| 33862 | 3 | -5 | -211 | 412010 | 33862-3 | 8 |
| 42684 | 1 | 114 | 211 | 413275 | 42684-1 | 8 |
| 19427 | 0 | -12 | -211 | 426433 | 19427-0 | 8 |
| 15154 | 1 | 21 | 211 | 428002 | 15154-1 | 8 |
| 17148 | 0 | -73 | -211 | 430653 | 17148-0 | 8 |
| 26644 | 2 | -89 | -211 | 437918 | 26644-2 | 8 |
| 42684 | 1 | -17 | -211 | 438097 | 42684-1 | 8 |
| 42684 | 1 | -5 | -211 | 440170 | 42684-1 | 8 |
| 17148 | 0 | -7 | -211 | 455330 | 17148-0 | 8 |
| 19427 | 0 | 24 | 211 | 465098 | 19427-0 | 8 |
| 33862 | 3 | -150 | -211 | 479360 | 33862-3 | 8 |
| 42684 | 1 | -5 | -211 | 481628 | 42684-1 | 8 |
| 29214 | 0 | 36 | 211 | 484798 | 29214-0 | 8 |
| 19427 | 0 | 5 | 211 | 488904 | 19427-0 | 8 |
| 33862 | 3 | -24 | -211 | 501165 | 33862-3 | 8 |
| 467 | 1 | -44 | -211 | 508527 | 467-1 | 8 |
| 467 | 1 | -44 | -211 | 522240 | 467-1 | 8 |
| 19427 | 0 | -1 | -211 | 549553 | 19427-0 | 8 |
| 26644 | 2 | -14 | -211 | 551685 | 26644-2 | 8 |
| 42684 | 1 | 7 | -11 | 564312 | 42684-1 | 8 |
| 17148 | 0 | -14 | -211 | 581992 | 17148-0 | 8 |
| 467 | 1 | 1 | 211 | 593701 | 467-1 | 8 |
| 15154 | 1 | 19 | 211 | 593856 | 15154-1 | 8 |
| 31005 | 1 | -59 | -211 | 608925 | 31005-1 | 8 |