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Beide Seiten der vorigen Revision Vorhergehende Überarbeitung Nächste Überarbeitung | Vorhergehende Überarbeitung | ||
electrical_engineering_2:the_time-dependent_magnetic_field [2024/04/29 23:31] mexleadmin |
electrical_engineering_2:the_time-dependent_magnetic_field [2024/05/07 03:52] (aktuell) mexleadmin [Rod in Circuit] |
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Zeile 62: | Zeile 62: | ||
The SI unit for magnetic flux is the $\rm Weber$ (Wb), \begin{align*} [\Phi_{\rm m}] = [B] \cdot [A] = 1 ~\rm T \cdot m^2 = 1 ~ Wb \end{align*} | The SI unit for magnetic flux is the $\rm Weber$ (Wb), \begin{align*} [\Phi_{\rm m}] = [B] \cdot [A] = 1 ~\rm T \cdot m^2 = 1 ~ Wb \end{align*} | ||
- | Occasionally, the magnetic field unit is expressed as Weber per square meter ($\rm Wb/m^2$) instead of teslas, based on this definition. | + | Based on this definition, the magnetic field unit is occasionally |
In many practical applications, | In many practical applications, | ||
Each turn experiences the same magnetic flux $\Phi_{\rm m}$. | Each turn experiences the same magnetic flux $\Phi_{\rm m}$. | ||
Zeile 139: | Zeile 139: | ||
To use Lenz’s law to determine the directions of induced potential difference, currents, and magnetic fields: | To use Lenz’s law to determine the directions of induced potential difference, currents, and magnetic fields: | ||
- | - Make a sketch of the situation | + | - Make a sketch of the situation |
- Determine the direction of the applied magnetic field $\vec{B}$. | - Determine the direction of the applied magnetic field $\vec{B}$. | ||
- Determine whether the magnitude of its magnetic flux is increasing or decreasing. | - Determine whether the magnitude of its magnetic flux is increasing or decreasing. | ||
- | - Now determine the direction of the induced magnetic field $\vec{B_{\rm ind}}$. The induced magnetic field tries to reinforce | + | - Now determine the direction of the induced magnetic field $\vec{B_{\rm ind}}$. |
- Use the right-hand rule to determine the direction of the induced current $i_{\rm ind}$ that is responsible for the induced magnetic field $\vec{B}_{\rm ind}$. | - Use the right-hand rule to determine the direction of the induced current $i_{\rm ind}$ that is responsible for the induced magnetic field $\vec{B}_{\rm ind}$. | ||
- The direction (or polarity) of the induced potential difference can now drive a conventional current in this direction. | - The direction (or polarity) of the induced potential difference can now drive a conventional current in this direction. | ||
Zeile 371: | Zeile 371: | ||
\begin{align*} | \begin{align*} | ||
- | u_{\rm ind} &= N B \cdot \sin \varphi \cdot {{{\rm d} \varphi}\over{{\rm d}t}} | + | u_{\rm ind} &= N B A \cdot \sin \varphi \cdot {{{\rm d} \varphi}\over{{\rm d}t}} |
\end{align*} | \end{align*} | ||
</ | </ | ||
Zeile 377: | Zeile 377: | ||
<button size=" | <button size=" | ||
- | We are given that $N=200$, $B=0.80~\rm T$ , $\varphi = 90°$ , $d\varphi=90°=\pi/ | + | We are given that $N=200$, $B=0.80~\rm T$ , $\varphi = 90°$ , $\Delta\varphi=90°=\pi/ |
The area of the loop is | The area of the loop is | ||
Zeile 504: | Zeile 504: | ||
Once the simulation is started, the inductor directly counteracts the current, which is why the current only slowly increases. | Once the simulation is started, the inductor directly counteracts the current, which is why the current only slowly increases. | ||
- | The unit of the inductance is $\rm 1 Henry = 1 H = {{Vs}\over{A}} = {{Wb}\over{A}} $ | + | The unit of the inductance is $\rm 1 ~Henry = 1 ~H = 1 {{Vs}\over{A}} = 1{{Wb}\over{A}} $ |
< | < |