Commit ea1ce5d2 authored by Stefan Gehr's avatar Stefan Gehr
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2d ohne Zwischenergebnisse

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......@@ -102,12 +102,16 @@ Geht man jedoch davon aus, dass es sich in einem Inertialsystem befindet, dann e
= \SI{1.2070231890599434e-08}{\second}
.\end{align*}
\subsection{}
Mit \(p = \gamma m v\), \(\gamma = E_{\mathrm{kin}}/(mc^2)+1\)
und \(v=c\sqrt{1-\frac{1}{\gamma^2}} = c\sqrt{1-\left(E_{\mathrm{kin}}/(mc^2)+1\right)^{-2}}\) erhält man \[
p = \left(\frac{E_{\mathrm{kin}}}{mc^2}+1\right)mc\sqrt{1-\left(\frac{E_{\mathrm{kin}}}{mc^2}+1\right)^{-2}}
.\]
\begin{align*}
p
&= qBR \\
B &= \frac{p}{qR} = \frac{2\pi \,p}{e \, s}
= \frac{2\pi \, \gamma m_{\mathrm{P}}v}{e \, s}
= \SI{5.4344005536195334}{\tesla} \\
B &= \frac{p}{qR}
= \frac{2\pi}{e \, s}\left(\frac{E_{\mathrm{kin}}}{mc^2}+1\right)mc\sqrt{1-\left(\frac{E_{\mathrm{kin}}}{mc^2}+1\right)^{-2}}
= \SI{5.434400553619534}{\tesla}
&\approx \SI{5.4}{\tesla}
.\end{align*}
\section{Invariante Masse}
......
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