Cosmic rays *
The most extremely relativistic charged particles we know about are cosmic rays which arrive from outer space. Occasionally one of these particles has so much kinetic energy that it can initiate in the atmosphere a ``giant shower'' of secondary particles, dissipating, in total, as much as 1019 eV of energy (more than 1 joule!). The primary particle, probably a proton, must have had γ≈1010. How far away from such a proton would the field rise to 1 V/m as it passes? Roughly how thick is the ``pancake'' of field lines at that distance? (You can use the result from either Problem 5.6 or Exercise 5.21 that the angular width of the pancake is on the order of 1/γ.)