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wallscheid committed Jul 29, 2024
2 parents 2832d30 + 73bdd18 commit 5d3ef24
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16 changes: 8 additions & 8 deletions exercise/tex/exercise01.tex
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As the conductor is flexibly connected to the battery via flexible connections the force $F$ in the air gap accelerates it to the right in its direction.

\begin{figure}[ht]
\begin{solutionfigure}[ht]
\centering
\includegraphics{ex01/solution_LorentzForce.pdf}
\caption{Acting Lorentz force on the conductor in the air gap.}
\label{fig:solution_LorentzForce}
\end{figure}
\end{solutionfigure}

\end{solutionblock}

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As long as $v B_{\updelta} l$ is less than $U_{\mathrm{B0}}$, is $I$ > 0 and the driving force $F$ > 0 remains effective. The induced voltage acts against the current direction $I$, which is the cause of the conductor movement through $F$, and therefore acts against the cause of its creation (Lenz's rule, Fig.~\ref{fig:solution_movingConductor}).

\begin{figure}[ht]
\begin{solutionfigure}[ht]
\centering
\includegraphics{ex01/solution_movingConductor.pdf}
\caption{Moving conductor with the induced voltage $u_{\mathrm{i}}$ as an external voltage, a) equivalent electrical circuit diagram, b) direction of the Lorentz force $F$.}
\label{fig:solution_movingConductor}
\end{figure}
\end{solutionfigure}

\end{solutionblock}

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\end{equation}

The Lorentz force and the friction force are visualized in Fig.~\ref{fig:solution_LorentzForce_balanceOfForces} after reaching the final speed.
\begin{figure}[ht]
\begin{solutionfigure}[ht]
\centering
\includegraphics{ex01/solution_LorentzForce_balanceOfForces.pdf}
\caption{Indicates the balance of forces after reaching the final speed.}
\label{fig:solution_LorentzForce_balanceOfForces}
\end{figure}
\end{solutionfigure}

\end{solutionblock}

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F = I l B_{\updelta},
\end{equation}
and the resulting values are shown in der right part of Fig.~\ref{fig:solution_conductorSpeed}.
\begin{figure}[ht]
\begin{solutionfigure}[ht]
\centering
\includegraphics{ex01/solution_conductorSpeed.pdf}
\caption{Current and force of the conductor in relationship to the velocity.}
\label{fig:solution_conductorSpeed}
\end{figure}
\end{solutionfigure}

\end{solutionblock}

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