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electrical_engineering_and_electronics_1:block20 [2025/12/02 18:50] – mexleadminelectrical_engineering_and_electronics_1:block20 [2025/12/16 14:14] (aktuell) – mexleadmin
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-====== Block 20 — Electromagnetic Induction and Energy ======+====== Block 20 — Inductance and Energy ======
  
 ===== Learning objectives ===== ===== Learning objectives =====
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 <WRAP> <imgcaption ImgNr15 | Self-Induction of a Coil> </imgcaption> {{drawio>SelfInductionCoil.svg}} </WRAP> <WRAP> <imgcaption ImgNr15 | Self-Induction of a Coil> </imgcaption> {{drawio>SelfInductionCoil.svg}} </WRAP>
  
-The created field density of the coil can be derived from Ampere's Circuital Law +Given by the [[block16#Recap of the fieldline images]] in Block16, we know that the $H$-field is given by magnetic voltage $\theta(t) = N \cdot i$ as:
 \begin{align*}  \begin{align*} 
-\theta(t) &= \int & \vec{H}(t) \cdot {\rm d}\vec{s} \\  +   {H}(t) &=                         {{N \cdot i }\over {l}} \\ 
-          &= \int & \vec{H}_{\rm inner}(t) \cdot {\rm d}\vec{s} & + & \int \vec{H}_{\rm outer}(t) \cdot {\rm d} \vec{s} \\  +
-          &= \int & \vec{H}(t) \cdot {\rm d}\vec{s}             & + &   0 \\  +
-          &=      & {H}(t) \cdot l \\ +
 \end{align*} \end{align*}
  
-With magnetic voltage $\theta(t) = N \cdot i$ this lead to the magnetic flux density $B(t)$+This lead to the magnetic flux density $B(t)$
  
 \begin{align*}  \begin{align*} 
-N \cdot i &= {H}(t) \cdot l \\  
-   {H}(t) &=                         {{N \cdot i }\over {l}} \\  
    {B}(t) &= \mu_0 \mu_{\rm r} \cdot {{N \cdot i }\over {l}} \\     {B}(t) &= \mu_0 \mu_{\rm r} \cdot {{N \cdot i }\over {l}} \\ 
 \end{align*} \end{align*}
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 \end{align*} \end{align*}
  
-The changing flux $\Phi$ is now creating an induced electric voltage and current, which counteracts the initial change of the current. +The changing flux $\Phi$ is now creating an induced electric voltage and current, which counteracts the initial change of the current. \\
 This effect is called **Self Induction**. The induced electric voltage $u_{\rm ind}$ is given by: This effect is called **Self Induction**. The induced electric voltage $u_{\rm ind}$ is given by:
  
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 \end{align*} \end{align*}
  
-The result means that the induced electric voltage $u_{\rm ind}$ is proportional to the change of the current ${{\rm d}\over{{\rm d}t}}i$. +The result means that the induced electric voltage $u_{\rm ind}$ is proportional to the change of the current ${{\rm d}\over{{\rm d}t}}i$. \\
 The proportionality factor is also called **Self-inductance**  $L$ (or often simply called inductance). The proportionality factor is also called **Self-inductance**  $L$ (or often simply called inductance).