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electrical_engineering_and_electronics_1:block09 [2025/10/20 02:57] – mexleadminelectrical_engineering_and_electronics_1:block09 [2025/10/20 03:06] (aktuell) – mexleadmin
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 {{url>https://phet.colorado.edu/sims/html/john-travoltage/latest/john-travoltage_de.html 500,400 noborder}} {{url>https://phet.colorado.edu/sims/html/john-travoltage/latest/john-travoltage_de.html 500,400 noborder}}
 </WRAP> </WRAP>
- 
-We had already considered the charge as the central quantity of electricity in the first chapter of the previous semester and recognized it as a multiple of the elementary charge. There was already a mutual force action ([[electrical_engineering_1:preparation_properties_proportions#coulomb-force|the Coulomb-force]]) derived. This will be more fully explained. 
  
 First, we shall define certain terms: First, we shall define certain terms:
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 ==== The electric Field ==== ==== The electric Field ====
  
-To determine the electric field, a measurement of its magnitude and direction is now required. The Coulomb force between two charges $Q_1$ and $Q_2$ is known from the first chapter of the previous semester:+We had already considered the charge as the central quantity of electricity in [[block02]] and recognized it as a multiple of the elementary charge.  
 +Now, we want to determine the electric field of charges. For this, a measurement of its magnitude and direction is now required. The **Coulomb force** between two charges $Q_1$ and $Q_2$ is:
  
 \begin{align*} \begin{align*}
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 The direction of the electric field is switchable in <imgref ImgNr02> via the "Electric Field" option on the right. \\ The direction of the electric field is switchable in <imgref ImgNr02> via the "Electric Field" option on the right. \\
  
 +
 +==== Direction of the Coulomb force and Superposition ====
 +
 +In the case of the force, only the direction has been considered so far, e.g., direction towards the sample charge. For future explanations, it is important to include the cause and effect in the naming. This is done by giving the correct labeling of the subscript of the force. In <imgref ImgNr06> (a) and (b), the convention is shown: A force $\vec{F}_{21}$ acts on charge $Q_2$ and is caused by charge $Q_1$. As a mnemonic, you can remember "tip-to-tail" (first the effect, then the cause).
 +
 +Furthermore, several forces on a charge can be superimposed, resulting in a single, equivalent force. \\
 +Strictly speaking, it must hold that $\varepsilon$ is constant in the structure. For example, the resultant force in <imgref ImgNr06> Fig. (c) on $Q_3$ becomes equal to: $\vec{F_3}= \vec{F_{31}}+\vec{F_{32}}$.
 +
 +<WRAP>
 +<imgcaption ImgNr06 | direction of coulomb force>
 +</imgcaption> <WRAP>.
 +{{drawio>DirectionOfCoulombforce.svg}} \\
 +</WRAP>
 +
 +~~PAGEBREAK~~ ~~CLEARFIX~~
 +==== Geometric Distribution of Charges ====
 +
 +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.
 +  * 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, this also applies to an extended charged object, which has exactly an extension that is no longer small in relation to the distance. For this purpose, the charge $Q$ is considered to be distributed over the line. Thus, a (line) charge density $\rho_l$ can be determined: <WRAP centeralign>$\rho_l = {{Q}\over{l}}$</WRAP> or, in the case of different charge densities on subsections: <WRAP centeralign>$\rho_l = {{\Delta Q}\over{\Delta l}} \rightarrow \rho_l(l)={{\rm d}\over{{\rm d}l}} Q(l)$</WRAP>
 +  * It is spoken of as an **area charge** when the charge is distributed over an area. \\ Examples of this are the floor or the 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>$\rho_A = {{Q}\over{A}}$</WRAP> or if there are different charge densities on partial surfaces: <WRAP centeralign>$\rho_A = {{\Delta Q}\over{\Delta A}} \rightarrow \rho_A(A) ={{\rm d}\over{{\rm d}A}} Q(A)={{\rm d}\over{{\rm d}x}}{{\rm d}\over{{\rm d}y}} Q(A)$</WRAP>
 +  * 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, a (space) charge density $\rho_V$ can be calculated here: <WRAP centeralign>$\rho_V = {{Q}\over{V}}$</WRAP> or for different charge density in partial volumes: <WRAP centeralign>$\rho_V = {{\Delta Q}\over{\Delta V}} \rightarrow \rho_V(V) ={{\rm d}\over{{\rm d}V}} Q(V)={{\rm d}\over{{\rm d}x}}{{\rm d}\over{{\rm d}y}}{{\rm d}\over{{\rm d}z}} Q(V)$</WRAP>
  
 ==== Electric Field Lines ==== ==== Electric Field Lines ====
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 ~~PAGEBREAK~~ ~~CLEARFIX~~ ~~PAGEBREAK~~ ~~CLEARFIX~~
- +==== Types of Fields depending on the Charge Distribution ====
-==== Electric Charge and Coulomb Force (reloaded) ==== +
- +
-The electric charge and Coulomb force have already been described last semester. However, some points are to be caught up here. +
- +
-=== Direction of the Coulomb force and Superposition === +
- +
-In the case of the force, only the direction has been considered so far, e.g., direction towards the sample charge. For future explanations, it is important to include the cause and effect in the naming. This is done by giving the correct labeling of the subscript of the force. In <imgref ImgNr06> (a) and (b), the convention is shown: A force $\vec{F}_{21}$ acts on charge $Q_2$ and is caused by charge $Q_1$. As a mnemonic, you can remember "tip-to-tail" (first the effect, then the cause). +
- +
-Furthermore, several forces on a charge can be superimposed, resulting in a single, equivalent force. \\ +
-Strictly speaking, it must hold that $\varepsilon$ is constant in the structure. For example, the resultant force in <imgref ImgNr06> Fig. (c) on $Q_3$ becomes equal to: $\vec{F_3}= \vec{F_{31}}+\vec{F_{32}}$. +
- +
-<WRAP> +
-<imgcaption ImgNr06 | direction of coulomb force> +
-</imgcaption> <WRAP>. +
-{{drawio>DirectionOfCoulombforce.svg}} \\ +
-</WRAP> +
- +
-~~PAGEBREAK~~ ~~CLEARFIX~~ +
-=== Geometric Distribution of Charges === +
- +
-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. +
-  * 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, this also applies to an extended charged object, which has exactly an extension that is no longer small in relation to the distance. For this purpose, the charge $Q$ is considered to be distributed over the line. Thus, a (line) charge density $\rho_l$ can be determined: <WRAP centeralign>$\rho_l = {{Q}\over{l}}$</WRAP> or, in the case of different charge densities on subsections: <WRAP centeralign>$\rho_l = {{\Delta Q}\over{\Delta l}} \rightarrow \rho_l(l)={{\rm d}\over{{\rm d}l}} Q(l)$</WRAP> +
-  * It is spoken of as an **area charge** when the charge is distributed over an area. \\ Examples of this are the floor or the 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>$\rho_A = {{Q}\over{A}}$</WRAP> or if there are different charge densities on partial surfaces: <WRAP centeralign>$\rho_A = {{\Delta Q}\over{\Delta A}} \rightarrow \rho_A(A) ={{\rm d}\over{{\rm d}A}} Q(A)={{\rm d}\over{{\rm d}x}}{{\rm d}\over{{\rm d}y}} Q(A)$</WRAP> +
-  * 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, a (space) charge density $\rho_V$ can be calculated here: <WRAP centeralign>$\rho_V = {{Q}\over{V}}$</WRAP> or for different charge density in partial volumes: <WRAP centeralign>$\rho_V = {{\Delta Q}\over{\Delta V}} \rightarrow \rho_V(V) ={{\rm d}\over{{\rm d}V}} Q(V)={{\rm d}\over{{\rm d}x}}{{\rm d}\over{{\rm d}y}}{{\rm d}\over{{\rm d}z}} Q(V)$</WRAP> +
- +
-In the following, area charges and their interactions will be considered. +
- +
-=== Types of Fields depending on the Charge Distribution ===+
  
 There are two different types of fields: There are two different types of fields: