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schaefera

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**"Flux in Through/ Out of Caps" Purcell**

## Homework Statement

I'm working problem 5.11 in Purcell's E&M book. It's about relativistic particles, and the eventual condition about angles at which the E-field lines are directed. The ultimate goal is to prove that tan([itex]\varphi[/itex])=[itex]\gamma[/itex]tan([itex]\theta[/itex]).

## Homework Equations

## The Attempt at a Solution

I have solved the integral for the "inner cap's" flux, and got that Flux1=2[itex]\pi[/itex]Q(1-cos[itex]\theta[/itex]).

The "outer cap" flux is Flux2=2[itex]\pi[/itex]Q(1-[itex]\gamma[/itex]cot([itex]\varphi[/itex]). (This integral might not be correct, though...)

I'm missing a sin([itex]\theta[/itex]) somewhere in the first flux, but I don't know where it could be.

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