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electrical_engineering_2:the_electrostatic_field [2023/05/12 13:35] mexleadmin |
electrical_engineering_2:the_electrostatic_field [2024/07/01 13:08] (aktuell) mexleadmin [Bearbeiten - Panel] |
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Zeile 1: | Zeile 1: | ||
- | ====== 1. The Electrostatic Field ====== | + | ====== 1 The Electrostatic Field ====== |
< | < | ||
Zeile 9: | Zeile 9: | ||
</ | </ | ||
- | From everyday | + | Everyday |
< | < | ||
< | < | ||
Zeile 17: | Zeile 16: | ||
</ | </ | ||
- | In the first chapter of the last semester, we had already considered the charge as the central quantity of electricity and understood | + | We had already considered the charge as the central quantity of electricity |
- | First, we will differentiate some terms: | + | First, we shall define certain |
- | - **{{wp> | + | - **{{wp> |
- | - **{{wp> | + | - **{{wp> |
- | - **{{wp> | + | - **{{wp> |
- | In this chapter, only electrostatics are considered. The magnetic fields are therefore | + | Only electrostatics is discussed in this chapter. |
- | Also, electrodynamics is not considered | + | Furthermore, electrodynamics is not covered |
~~PAGEBREAK~~ ~~CLEARFIX~~ | ~~PAGEBREAK~~ ~~CLEARFIX~~ | ||
Zeile 52: | Zeile 51: | ||
<panel type=" | <panel type=" | ||
- | The simulation in <imgref ImgNr02> | + | The simulation in was already |
- | In the simulation, please position | + | Place a negative charge $Q$ in the middle |
- | For impact analysis, a sample charge $q$ is placed | + | A sample charge $q$ is placed |
< | < | ||
Zeile 65: | Zeile 64: | ||
</ | </ | ||
- | The concept of a field shall now be briefly | + | The concept of a field will now be briefly |
- | - The introduction of the field separates | + | - The introduction of the field distinguishes |
- | - The charge $Q$ causes the field in space. | + | - The field in space is caused by the charge $Q$. |
- | - The charge $q$ in space feels a force as an effect of the field. | + | - As a result of the field, the charge $q$ in space feels a force. |
- | - This distinction | + | - This distinction |
- | - As with physical quantities, there are different-dimensional fields: | + | -There are different-dimensional fields, just like physical quantities: |
- | - In a **scalar field**, | + | - In a **scalar field**, each point in space is assigned a single number. \\ For example, |
- | - temperature field $T(\vec{x})$ on the weather map or in an object | + | - a temperature field $T(\vec{x})$ on a weather map or in an object |
- | - pressure field $p(\vec{x})$ | + | - a pressure field $p(\vec{x})$ |
- | - In a **vector field**, each point in space is assigned several numbers in the form of a vector. This reflects the action along the spatial coordinates. \\ For example. | + | - Each point in space in a **vector field** is assigned several numbers in the form of a vector. This reflects the action |
- | - gravitational field $\vec{g}(\vec{x})$ pointing to the center of mass of the object. | + | - gravitational field $\vec{g}(\vec{x})$ pointing to the object' |
- electric field $\vec{E}(\vec{x})$ | - electric field $\vec{E}(\vec{x})$ | ||
- magnetic field $\vec{H}(\vec{x})$ | - magnetic field $\vec{H}(\vec{x})$ | ||
- | - If each point in space is associated with a two- or more-dimensional physical quantity - that is a tensor | + | - A tensor field is one in which each point in space is associated with a two- or more-dimensional physical quantity - that is, a tensor. Tensor fields are useful |
- | Vector fields | + | Vector fields |
- Effects along spatial axes $x$, $y$ and $z$ (Cartesian coordinate system). | - Effects along spatial axes $x$, $y$ and $z$ (Cartesian coordinate system). | ||
- Effect in magnitude and direction vector (polar coordinate system) | - Effect in magnitude and direction vector (polar coordinate system) | ||
Zeile 92: | Zeile 91: | ||
==== The Electric Field ==== | ==== The Electric Field ==== | ||
- | Thus, to determine the electric field, a measure | + | To determine the electric field, a measurement |
\begin{align*} | \begin{align*} | ||
Zeile 98: | Zeile 97: | ||
\end{align*} | \end{align*} | ||
- | To obtain a measure of the magnitude of the electric field, the force on a (fictitious) sample charge $q$ is now considered. | + | The force on a (fictitious) sample charge $q$ is now considered |
\begin{align*} | \begin{align*} | ||
Zeile 105: | Zeile 104: | ||
\end{align*} | \end{align*} | ||
- | The left part is therefore | + | As a result, the left part is a measure of the magnitude of the field, independent of the size of the sample charge $q$. Thus, the magnitude of the electric field is given by |
<WRAP centeralign> | <WRAP centeralign> | ||
Zeile 119: | Zeile 118: | ||
<callout icon=" | <callout icon=" | ||
- | - The test charge $q$ is always considered to be posi**__t__**ive (mnemonic: t = +). It is used only as a thought experiment and has no retroactive effect on the sampled charge $Q$. | + | - The test charge $q$ is always considered to be posi**__t__**ive (mnemonic: t = +). It is only used as a thought experiment and has no retroactive effect on the sampled charge $Q$. |
- The sampled charge here is always a point charge. | - The sampled charge here is always a point charge. | ||
</ | </ | ||
Zeile 125: | Zeile 124: | ||
<callout icon=" | <callout icon=" | ||
- | A charge $Q$ generates | + | At a measuring point $P$, a charge $Q$ produces |
- the magnitude $|\vec{E}|=\Bigl| {{1} \over {4\pi\cdot\varepsilon}} \cdot {{Q_1} \over {r^2}} \Bigl| $ and | - the magnitude $|\vec{E}|=\Bigl| {{1} \over {4\pi\cdot\varepsilon}} \cdot {{Q_1} \over {r^2}} \Bigl| $ and | ||
- | - the direction of the force $\vec{F_C}$ | + | - the direction of the force $\vec{F_C}$ |
- | Be aware, that in English courses and literature $\vec{E}, $ is simply | + | Be aware, that in English courses and literature $\vec{E}, $ is simply |
</ | </ | ||
Zeile 199: | Zeile 198: | ||
</ | </ | ||
- | <panel type=" | + | <panel type=" |
Sketch the field line plot for the charge configurations given in <imgref ImgNr04> | Sketch the field line plot for the charge configurations given in <imgref ImgNr04> | ||
Zeile 256: | Zeile 255: | ||
In previous chapters, only single charges (e.g. $Q_1$, $Q_2$) were considered. | In previous chapters, only single charges (e.g. $Q_1$, $Q_2$) were considered. | ||
* The charge $Q$ was previously reduced to a **point charge**. \\ This can be used, for example, for the elementary charge or for extended charged objects from a large distance. The distance is sufficiently large if the ratio between the largest object extent and the distance to the measurement point $P$ is small. | * The charge $Q$ was previously reduced to a **point charge**. \\ This can be used, for example, for the elementary charge or for extended charged objects from a large distance. The distance is sufficiently large if the ratio between the largest object extent and the distance to the measurement point $P$ is small. | ||
- | * If the charges are lined up along a line, this is called | + | * If the charges are lined up along a line, this is referred to as a **line charge**. \\ Examples of this are a straight trace on a circuit board or a piece of wire. Furthermore, |
* It is spoken of as an **area charge** when the charge is distributed over an area. \\ Examples of this are the floor or a plate of a capacitor. Again, an extended charged object can be considered when two dimensions are no longer small in relation to the distance (e.g. surface of the earth). Again, a (surface) charge density $\rho_A$ can be determined: <WRAP centeralign> | * It is spoken of as an **area charge** when the charge is distributed over an area. \\ Examples of this are the floor or a plate of a capacitor. Again, an extended charged object can be considered when two dimensions are no longer small in relation to the distance (e.g. surface of the earth). Again, a (surface) charge density $\rho_A$ can be determined: <WRAP centeralign> | ||
* Finally, a **space charge** is the term for charges that span a volume. \\ Here examples are plasmas or charges in extended objects (e.g. the doped volumes in a semiconductor). As with the other charge distributions, | * Finally, a **space charge** is the term for charges that span a volume. \\ Here examples are plasmas or charges in extended objects (e.g. the doped volumes in a semiconductor). As with the other charge distributions, | ||
Zeile 301: | Zeile 300: | ||
{{youtube> | {{youtube> | ||
</ | </ | ||
+ | |||
+ | {{page> | ||
+ | {{page> | ||
+ | {{page> | ||
+ | |||
=====1.3 Work and Potential ===== | =====1.3 Work and Potential ===== | ||
Zeile 420: | Zeile 424: | ||
- Returning to the starting point from any point $A$ after a closed circuit, the __circuit voltage__ along the closed path is 0. \\ A closed path is mathematically expressed as a ring integral: \begin{align} U = \oint \vec{E} \cdot {\rm d} \vec{s} = 0 \end{align} | - Returning to the starting point from any point $A$ after a closed circuit, the __circuit voltage__ along the closed path is 0. \\ A closed path is mathematically expressed as a ring integral: \begin{align} U = \oint \vec{E} \cdot {\rm d} \vec{s} = 0 \end{align} | ||
- Or spoken differently: | - Or spoken differently: | ||
- | - A field $\vec{X}$ which satisfies the condition $\oint \vec{X} \cdot {\rm d} \vec{s}=0$ is called | + | - A field $\vec{X}$ which satisfies the condition $\oint \vec{X} \cdot {\rm d} \vec{s}=0$ is referred to as __vortex-free__ or __potential field__. \\ From the potential difference, or the voltage, the work in the electrostatic field results as: \begin{align*} \boxed{W_{ \rm AB}= q \cdot U_{ \rm AB}} \end{align*} |
</ | </ | ||
Zeile 435: | Zeile 439: | ||
Once a charge $q$ moves perpendicular to the field lines, it experiences neither energy gain nor loss. | Once a charge $q$ moves perpendicular to the field lines, it experiences neither energy gain nor loss. | ||
The voltage along this path is $0~{ \rm V}$. All points where the voltage of $0~{ \rm V}$ is applied are at the same potential level. | The voltage along this path is $0~{ \rm V}$. All points where the voltage of $0~{ \rm V}$ is applied are at the same potential level. | ||
- | The connection of these points | + | The connection of these points |
* equipotential lines for a 2-dimensional representation of the field. | * equipotential lines for a 2-dimensional representation of the field. | ||
* equipotential surfaces for a 3-dimensional field | * equipotential surfaces for a 3-dimensional field | ||
Zeile 522: | Zeile 526: | ||
</ | </ | ||
- | |||
- | ==== Tasks ==== | ||
- | |||
- | {{page> | ||
- | {{page> | ||
- | {{page> | ||
=====1.4 Conductors in the Electrostatic Field ===== | =====1.4 Conductors in the Electrostatic Field ===== | ||
Zeile 623: | Zeile 621: | ||
* The field lines leave the surface again at right angles. Again, a parallel component would cause a charge shift in the metal. | * The field lines leave the surface again at right angles. Again, a parallel component would cause a charge shift in the metal. | ||
- | This effect of charge displacement in conductive objects by an electrostatic field is called | + | This effect of charge displacement in conductive objects by an electrostatic field is referred to as **electrostatic induction** (in German: // |
Induced charges can be separated (<imgref ImgNr11> right). | Induced charges can be separated (<imgref ImgNr11> right). | ||
If we look at the separated induced charges without the external field, their field is again just as strong in magnitude as the external field only in the opposite direction. | If we look at the separated induced charges without the external field, their field is again just as strong in magnitude as the external field only in the opposite direction. | ||
Zeile 669: | Zeile 667: | ||
{{page> | {{page> | ||
+ | <wrap anchor # | ||
<panel type=" | <panel type=" | ||
Zeile 683: | Zeile 682: | ||
- | --> Answer | + | # |
$\varrho_2 < \varrho_3 < \varrho_1 < \varrho_4$ | $\varrho_2 < \varrho_3 < \varrho_1 < \varrho_4$ | ||
Zeile 690: | Zeile 689: | ||
< | < | ||
</ | </ | ||
- | {{url> | + | {{url> |
</ | </ | ||
- | <-- | + | |
+ | # | ||
+ | |||
</ | </ | ||
Zeile 898: | Zeile 901: | ||
An ideal plate capacitor with a distance of $d_0 = 6 ~{ \rm mm}$ between the plates and with air as dielectric ($\varepsilon_0=1$) is charged to a voltage of $U_0 = 5~{ \rm kV}$. | An ideal plate capacitor with a distance of $d_0 = 6 ~{ \rm mm}$ between the plates and with air as dielectric ($\varepsilon_0=1$) is charged to a voltage of $U_0 = 5~{ \rm kV}$. | ||
- | The source remains connected to the capacitor. In the air gap between the plates, a glass plate with $d_{ \rm g} = 2 ~{ \rm mm}$ and $\varepsilon_{ \rm r} = 8$ is introduced parallel to the capacitor plates. | + | The source remains connected to the capacitor. In the air gap between the plates, a glass plate with $d_{ \rm g} = 4 ~{ \rm mm}$ and $\varepsilon_{ \rm r} = 8$ is introduced parallel to the capacitor plates. |
- | - Calculate the partial voltages on the glas $U_{ \rm g}$ and on the air gap $U_{ \rm a}$. | + | 1. Calculate the partial voltages on the glas $U_{ \rm g}$ and on the air gap $U_{ \rm a}$. |
- | - What would be the maximum allowed thickness of a glass plate, when the electric field in the air-gap shall not exceed $E_{ \rm max}=12~{ \rm kV/cm}$? | + | |
- | <button size=" | + | # |
* build a formula for the sum of the voltages first | * build a formula for the sum of the voltages first | ||
* How is the voltage related to the electric field of a capacitor? | * How is the voltage related to the electric field of a capacitor? | ||
- | </ | + | # |
- | <button size=" | + | # |
- | - $U_{ \rm a} = 4~{ \rm kV}$, $U_{ \rm g} = 1 ~{ \rm kV}$ | + | |
- | - $d_{ \rm g} = 5.96~{ \rm mm}$ | + | The sum of the voltages across the glass and the air gap gives the total voltage $U_0$ and each individual voltage is given by the $E$-field in the individual material by $E = {{U}\over{d}}$: |
- | </ | + | \begin{align*} |
+ | U_0 &= U_{\rm g} + U_{\rm a} \\ | ||
+ | &= E_{\rm g} \cdot d_{\rm g} + E_{\rm a} \cdot d_{\rm a} | ||
+ | \end{align*} | ||
+ | |||
+ | The displacement field $D$ must be continuous across the different materials since it is only based on the charge $Q$ on the plates. | ||
+ | \begin{align*} | ||
+ | D_{\rm g} &= D_{\rm a} \\ | ||
+ | \varepsilon_0 \varepsilon_{\rm r, g} \cdot E_{\rm g} &= \varepsilon_0 | ||
+ | \end{align*} | ||
+ | |||
+ | Therefore, we can put $E_\rm a= \varepsilon_{\rm r, g} \cdot E_\rm g $ into the formula of the total voltage and re-arrange to get $E_\rm g$: | ||
+ | \begin{align*} | ||
+ | U_0 &= E_{\rm g} \cdot d_{\rm g} + \varepsilon_{\rm r, g} \cdot E_{\rm g} \cdot d_{\rm a} \\ | ||
+ | &= E_{\rm g} \cdot ( d_{\rm g} + \varepsilon_{\rm r, g} \cdot d_{\rm a}) \\ | ||
+ | |||
+ | \rightarrow E_{\rm g} &= {{U_0}\over{d_{\rm g} + \varepsilon_{\rm r, g} \cdot d_{\rm a}}} | ||
+ | \end{align*} | ||
+ | |||
+ | Since we know that the distance of the air gap is $d_{\rm a} = d_0 - d_{\rm a}$ we can calculate: | ||
+ | \begin{align*} | ||
+ | E_{\rm g} &= {{5' | ||
+ | & | ||
+ | \end{align*} | ||
+ | |||
+ | By this, the individual voltages can be calculated: | ||
+ | \begin{align*} | ||
+ | U_{ \rm g} &= E_{\rm g} \cdot d_\rm g &&= 250 ~\rm{{kV}\over{m}} \cdot 0.004~\rm m &= 1 ~{\rm kV}\\ | ||
+ | U_{ \rm a} &= U_0 - U_{ \rm g} &&= 5 ~{\rm kV} - 1 ~{\rm kV} & | ||
+ | |||
+ | \end{align*} | ||
+ | # | ||
+ | |||
+ | |||
+ | # | ||
+ | $U_{ \rm a} = 4~{ \rm kV}$, $U_{ \rm g} = 1 ~{ \rm kV}$ | ||
+ | # | ||
+ | |||
+ | |||
+ | 2. What would be the maximum allowed thickness of a glass plate, when the electric field in the air-gap shall not exceed | ||
+ | |||
+ | # | ||
+ | Again, we can start with the sum of the voltages across the glass and the air gap, such as the formula we got from the displacement field: $D = \varepsilon_0 \varepsilon_{\rm r, g} \cdot E_{\rm g} = \varepsilon_0 | ||
+ | Now we shall eliminate $E_\rm g$, since $E_\rm a$ is given in the question. | ||
+ | \begin{align*} | ||
+ | U_0 & | ||
+ | &= {{E_\rm a}\over{\varepsilon_{\rm r, | ||
+ | \end{align*} | ||
+ | |||
+ | The distance $d_\rm a$ for the air is given by the overall distance $d_0$ and the distance for glass $d_\rm g$: | ||
+ | \begin{align*} | ||
+ | d_{\rm a} = d_0 - d_{\rm g} | ||
+ | \end{align*} | ||
+ | |||
+ | This results in: | ||
+ | \begin{align*} | ||
+ | U_0 &= {{E_{\rm a}}\over{\varepsilon_{\rm r,g}}} \cdot d_{\rm g} + E_{\rm a} \cdot (d_0 - d_{\rm g}) \\ | ||
+ | {{U_0}\over{E_{\rm a} }} &= {{1}\over{\varepsilon_{\rm r,g}}} \cdot d_{\rm g} + d_0 - d_{\rm g} \\ | ||
+ | & | ||
+ | d_{\rm g} &= { { {{U_0}\over{E_{\rm a} }} - d_0 } \over { {{1}\over{\varepsilon_{\rm r,g}}} - 1 } } & | ||
+ | \end{align*} | ||
+ | |||
+ | With the given values: | ||
+ | \begin{align*} | ||
+ | d_{\rm g} &= { { 0.006 {~\rm m} - {{5 {~\rm kV} }\over{ 12 {~\rm kV/cm}}} } \over { 1 - {{1}\over{8}} } } &= { {{8}\over{7}} } \left( { 0.006 - {{5 }\over{ 1200}} } \right) | ||
+ | \end{align*} | ||
+ | # | ||
+ | |||
+ | |||
+ | # | ||
+ | $d_{ \rm g} = 2.10~{ \rm mm}$ | ||
+ | # | ||
</ | </ | ||
Zeile 1007: | Zeile 1080: | ||
~~PAGEBREAK~~ ~~CLEARFIX~~ | ~~PAGEBREAK~~ ~~CLEARFIX~~ | ||
<callout icon=" | <callout icon=" | ||
- | - The material constant $\varepsilon_{ \rm r}$ is called | + | - The material constant $\varepsilon_{ \rm r}$ is referred to as relative permittivity, |
- Relative permittivity is unitless and indicates how much the electric field decreases with the presence of material for the same charge. | - Relative permittivity is unitless and indicates how much the electric field decreases with the presence of material for the same charge. | ||
- The relative permittivity $\varepsilon_{ \rm r}$ is always greater than or equal to 1 for dielectrics (i.e., nonconductors). | - The relative permittivity $\varepsilon_{ \rm r}$ is always greater than or equal to 1 for dielectrics (i.e., nonconductors). | ||
Zeile 1015: | Zeile 1088: | ||
<callout icon=" | <callout icon=" | ||
- | Suppose now the relative permittivity $\varepsilon_{ \rm r}$ depends on the possibility of aligning the molecules in the field. In that case, the following interesting relation arises: if frequencies are " | + | Suppose now the relative permittivity $\varepsilon_{ \rm r}$ depends on the possibility of aligning the molecules in the field. In that case, the following interesting relation arises: if frequencies are " |
</ | </ | ||
Zeile 1044: | Zeile 1117: | ||
* One says: The insulator breaks down. This means that above this electric field, a current can flow through the insulator. | * One says: The insulator breaks down. This means that above this electric field, a current can flow through the insulator. | ||
* Examples are: Lightning in a thunderstorm, | * Examples are: Lightning in a thunderstorm, | ||
- | * The maximum electric field $E_0$ is called | + | * The maximum electric field $E_0$ is referred to as ** dielectric strength** (in German: // |
* $E_0$ depends on the material (see <tabref tab02>), but also on other factors (temperature, | * $E_0$ depends on the material (see <tabref tab02>), but also on other factors (temperature, | ||
Zeile 1171: | Zeile 1244: | ||
- In the multilayer capacitor, there are again two electrodes. Here, too, the area $A$ (and thus the capacitance $C$) is multiplied by the finger-shaped interlocking. | - In the multilayer capacitor, there are again two electrodes. Here, too, the area $A$ (and thus the capacitance $C$) is multiplied by the finger-shaped interlocking. | ||
- Ceramic is used here as the dielectric. | - Ceramic is used here as the dielectric. | ||
- | - The multilayer ceramic capacitor is also called | + | - The multilayer ceramic capacitor is also referred to as KerKo or MLCC. |
- The variant shown in (2) is an SMD variant (surface mound device). | - The variant shown in (2) is an SMD variant (surface mound device). | ||
- Disk capacitor | - Disk capacitor | ||
- A ceramic is also used as a dielectric for the disk capacitor. This is positioned as a round disc between two electrodes. | - A ceramic is also used as a dielectric for the disk capacitor. This is positioned as a round disc between two electrodes. | ||
- Disc capacitors are designed for higher voltages, but have a low capacitance (in the microfarad range). | - Disc capacitors are designed for higher voltages, but have a low capacitance (in the microfarad range). | ||
- | - **{{wp> | + | - **{{wp> |
- In electrolytic capacitors, the dielectric is an oxide layer formed on the metallic electrode. the second electrode is the liquid or solid electrolyte. | - In electrolytic capacitors, the dielectric is an oxide layer formed on the metallic electrode. the second electrode is the liquid or solid electrolyte. | ||
- Different metals can be used as the oxidized electrode, e.g. aluminum, tantalum or niobium. | - Different metals can be used as the oxidized electrode, e.g. aluminum, tantalum or niobium. | ||
Zeile 1182: | Zeile 1255: | ||
- Important for the application is that it is a polarized capacitor. I.e. it may only be operated in one direction with DC voltage. Otherwise, a current can flow through the capacitor, which destroys it and is usually accompanied by an explosive expansion of the electrolyte. To avoid reverse polarity, the negative pole is marked with a dash. | - Important for the application is that it is a polarized capacitor. I.e. it may only be operated in one direction with DC voltage. Otherwise, a current can flow through the capacitor, which destroys it and is usually accompanied by an explosive expansion of the electrolyte. To avoid reverse polarity, the negative pole is marked with a dash. | ||
- The electrolytic capacitor is built up wrapped and often has a cross-shaped predetermined breaking point at the top for gas leakage. | - The electrolytic capacitor is built up wrapped and often has a cross-shaped predetermined breaking point at the top for gas leakage. | ||
- | - **{{wp> | + | - **{{wp> |
- A material similar to a "chip bag" is used as an insulator: a plastic film with a thin, metalized layer. | - A material similar to a "chip bag" is used as an insulator: a plastic film with a thin, metalized layer. | ||
- The construction shows a high pulse load capacitance and low internal ohmic losses. | - The construction shows a high pulse load capacitance and low internal ohmic losses. | ||
- In the event of electrical breakdown, the foil enables " | - In the event of electrical breakdown, the foil enables " | ||
- | - With some manufacturers, | + | - With some manufacturers, |
- **{{wp> | - **{{wp> | ||
- As a dielectric is - similar to the electrolytic capacitor - very thin. In the actual sense, there is no dielectric at all. | - As a dielectric is - similar to the electrolytic capacitor - very thin. In the actual sense, there is no dielectric at all. | ||
Zeile 1324: | Zeile 1397: | ||
\end{align*} | \end{align*} | ||
\begin{align*} | \begin{align*} | ||
- | \boxed{ U_k = const} | + | \boxed{ U_k = {\rm const.}} |
\end{align*} | \end{align*} | ||
</ | </ | ||
Zeile 1370: | Zeile 1443: | ||
- | Up to now was assumed only one dielectric | + | Up until this point, it was assumed |
- | Thereby several | + | By doing this, various |
- | The following | + | It is possible to tell the following |
- **layers are parallel to capacitor plates - dielectrics in series**: \\ The boundary layers are __parallel__ to the capacitor plates. \\ So, the different dielectrics are __perpendicular__ to the field lines. \\ \\ | - **layers are parallel to capacitor plates - dielectrics in series**: \\ The boundary layers are __parallel__ to the capacitor plates. \\ So, the different dielectrics are __perpendicular__ to the field lines. \\ \\ | ||
Zeile 1550: | Zeile 1623: | ||
</ | </ | ||
+ | <panel type=" | ||
+ | |||
+ | {{youtube> | ||
+ | |||
+ | </ | ||
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+ | <panel type=" | ||
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+ | {{youtube> | ||
+ | |||
+ | </ | ||
+ | |||
+ | <panel type=" | ||
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+ | {{youtube> | ||
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+ | </ | ||
- | <panel type=" | + | <panel type=" |
< | < |