so, hey...I'm pretty new to these forums and just needed help understanding a textbook that i'm reading.(adsbygoogle = window.adsbygoogle || []).push({});

I'll give you all the background, but I'm not sure if it is necessary.

They begin by considering a heavy particle of mass M and velocity v passing through a material with an atomic electron at distance b from the particle trajectory. the electron is assumed to be free and initially at rest. Furthermore, it is assumed that the electron only moves slightly during the interaction with the heavy particle. After the collision, it is assumed that the incident heavy particle continues essentially as before (because M>>me)

the impulse is calculated:

I=integral(Fdt)=e * integral(E_perpendicular)[tex]\frac{dt}{dx}[/tex]dx = e integral ( E_perpendicular [tex]\frac{dx}{v}[/tex]

They claim that only E_perpendicular enters because of symmetry. I am a little confused about this actually. I kind of reasoned it out by thinking of the work function (which would give the change in energy for the particle, right) W=integral(F . dx )=integral (eE . dx) = integral( e*E_perpendicular*dx)...(their next to last step seems kind of like this...)...but I think I'm just trying to make up something to understand it...so if anyone could tell me what symmetry they mean, I'd appreciate it.

Also, they go on to calculate the integral( E_perpendicular dx) using Gauss' Law over an infinitely long cylinder centered on the particle trajectory. They claim that:

integral ( E_perpendicular *2*pi*b*dx)=4*pi*z*e

I just don't know where the 4*pi is coming from on the right side (and where epsilon is..) and would really appreciate it if someone could explain this to me.

I hope this is an okay place to post this. It isn't homework, I'm just reading it...

I tried to draw the diagram from the book and it is attached (i hope).

I just feel like I must be missing something major

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# Bohr's calculation of stopping power

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