Focal length of electrostatic lens

The kinematics of the 2nd part is getting too messy to solve and I'm getting an extra factor of e^(pi/2). What am I doing wrong?
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@Gyro Gearloose
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Opt
Opt2mo ago
Lol Also, did you get it?
SirLancelotDuLac
SirLancelotDuLacOP2mo ago
Yeah I just realized d<<R means sin approximation 🤦‍♂️ But lets keep the thread open till I get the final answer :sweaty:
Opt
Opt2mo ago
Oh. 🤦‍♂️ In electric field component? Could I see your working for the first one?
SirLancelotDuLac
SirLancelotDuLacOP2mo ago
No, the second part. The note at the end of the paragraph tells you how to do the first part. Idk why I didn't read that lol,
Opt
Opt2mo ago
I didn't get it with the Gaussian surface too
SirLancelotDuLac
SirLancelotDuLacOP2mo ago
The first one was something like this. Also, ig we had to consider E_radial doesn't depend on z (as z is a very small quantity in relation to given scales).
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Opt
Opt2mo ago
Oh I see. Ok so focal distance huh
SirLancelotDuLac
SirLancelotDuLacOP2mo ago
That is just kinematic monstrocity ig :sweaty: Ye nvm. My method doesn't work lol. Any ideas?
Opt
Opt2mo ago
That's what I got too I was thinking if work energy theorem would work but idts
SirLancelotDuLac
SirLancelotDuLacOP2mo ago
Yep. +solved @Opt
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