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electrical_engineering_and_electronics_1:block17 [2025/12/02 17:36] – [Materials] mexleadminelectrical_engineering_and_electronics_1:block17 [2025/12/02 17:39] (aktuell) – [Applications of the Lorentz Force: Two parallel Conductors] mexleadmin
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 </WRAP></WRAP> </WRAP></WRAP>
  
-==== Applications of the Lorentz Force ==== +==== Applications of the Lorentz Force: Two parallel Conductors ===
- +
-We want to apply the Lorentz force for two common situations. +
- +
-<WRAP group><WRAP half column> +
- +
-=== Two parallel Conductors ===+
  
 The Lorentz force can be applied to two parallel conductors. \\  The Lorentz force can be applied to two parallel conductors. \\ 
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 \end{align*} \end{align*}
  
-</WRAP><WRAP half column> 
-=== Moving single Charge  === 
- 
-The true Lorentz force is not the force on the whole conductor but the single force onto an (elementary) charge. \\ 
-To find this force the previous force onto a conductor can be used as a start. However, the formula will be investigated infinitesimally for small parts ${\rm d} \vec{l}$ of the conductor: 
- 
-\begin{align*} 
-\vec{{\rm d}F}_{\rm L} = I \cdot {\rm d}\vec{l} \times \vec{B} 
-\end{align*} 
- 
-The current is now substituted by $I = {\rm d}Q/{\rm d}t$, where ${\rm d}Q$ is the small charge packet in the length $\vec{{\rm d}l}$ of the conductor. 
- 
-\begin{align*} 
-\vec{{\rm d}F}_{\rm L} = {{{\rm d}Q}\over{{\rm d}t}} \cdot {\rm d}\vec{l} \times \vec{B} 
-\end{align*} 
- 
-Mathematically not quite correct, but in a physical way true the following rearrangement can be done: 
- 
-\begin{align*} 
-\vec{{\rm d}F}_{\rm L} &= {{{\rm d}Q \cdot   {\rm d}\vec{l}}\over{{\rm d}t}} \times \vec{B} \\ 
-                       &= {\rm d}Q   \cdot {{{\rm d}\vec{l}}\over{{\rm d}t}} \times \vec{B} \\ 
-                       &= {\rm d}Q   \cdot {{{\rm d}\vec{l}}\over{{\rm d}t}} \times \vec{B} \\ 
-\end{align*} 
- 
-Here, the part ${{{\rm d}\vec{l}}\over{{\rm d}t}}$ represents the speed $\vec{v}$ of the small charge packet ${\rm d}Q$. 
- 
-\begin{align*} 
-\vec{{\rm d}F}_{\rm L} &= {\rm d}Q \cdot \vec{v} \times \vec{B}  
-\end{align*} 
- 
-The **Lorenz Force** on a finite charge packet is the integration: 
- 
-\begin{align*} 
-\boxed{\vec{F}_{\rm L} = Q \cdot \vec{v} \times \vec{B}} 
-\end{align*} 
- 
- 
- 
-<callout icon="fa fa-exclamation" color="red" title="Notice:"> 
- 
-  * A charge $Q$ moving with a velocity $\vec{v}$ in a magnetic field $\vec{B}$ experiences a force of $\vec{F_{\rm L}}$. 
-  * The direction of the force is given by the right-hand rule. 
- 
-</callout> 
- 
-</WRAP></WRAP>