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electrical_engineering_and_electronics_1:block09 [2025/10/27 00:54] – mexleadminelectrical_engineering_and_electronics_1:block09 [2026/01/10 13:00] (aktuell) – mexleadmin
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-====== Block 09 - Force on charges and electric field strength ======+====== Block 09 - Force on Charges and electric Field Strength ======
  
-~~PAGEBREAK~~ ~~CLEARFIX~~ +===== 9.0 Intro ===== 
-===== Learning objectives =====+ 
 +==== 9.0.1 Learning objectives ====
 <callout> <callout>
 By the end of this section, you will be able to: By the end of this section, you will be able to:
-  * Sketch the field lines of electric fields. 
   * Distinguish **charge** $Q$ (source) from **electric field** $\vec{E}$ (effect in space) and **force** $\vec{F}$ on a test charge $q$; use formula for Coulomb force with correct vector directions and units ($1~{\rm N/C}=1~{\rm V/m}$).   * Distinguish **charge** $Q$ (source) from **electric field** $\vec{E}$ (effect in space) and **force** $\vec{F}$ on a test charge $q$; use formula for Coulomb force with correct vector directions and units ($1~{\rm N/C}=1~{\rm V/m}$).
   * Explain and apply the **superposition principle** for forces and fields from multiple charges.   * Explain and apply the **superposition principle** for forces and fields from multiple charges.
-  * Describe and sketch **field lines** for single and multiple charges; relate line **density** to $|\vec{E}|$ and line **direction** to the force on a positive test charge. 
-  * Classify fields as **homogeneous** (e.g., parallel-plate region) or **inhomogeneous** (e.g., point charge); state typical properties near **conductors** (perpendicular boundary, field-free interior in electrostatics). 
   * Compute $|\vec{E}|$ for a **point charge** (Coulomb force), identify $\varepsilon$ and check dimensions.   * Compute $|\vec{E}|$ for a **point charge** (Coulomb force), identify $\varepsilon$ and check dimensions.
   * Determine the force on a charge in an electrostatic field by applying Coulomb's law. Specifically:   * Determine the force on a charge in an electrostatic field by applying Coulomb's law. Specifically:
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 </callout> </callout>
  
-===== 90-minute plan =====+~~PAGEBREAK~~ ~~CLEARFIX~~ 
 +==== 9.0.2 Preparation at Home ==== 
 + 
 +And again:  
 +  * Please read through the following chapter. 
 +  * Also here, there are some clips for more clarification under 'Embedded resources'.  
 + 
 +For checking your understanding please do the following exercise: 
 +  * 1.2.3 
 + 
 +~~PAGEBREAK~~ ~~CLEARFIX~~ 
 +==== 9.0.3 90-minute plan ====
   - Warm-up (8–10 min):   - Warm-up (8–10 min):
     - Quick recall quiz: units of $Q$, $\vec{E}$, $\vec{F}$; passive sign convention for forces on a **positive** test charge.     - Quick recall quiz: units of $Q$, $\vec{E}$, $\vec{F}$; passive sign convention for forces on a **positive** test charge.
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     - **Field lines**: definition, drawing rules, sources/sinks, no intersections; relate density to magnitude.     - **Field lines**: definition, drawing rules, sources/sinks, no intersections; relate density to magnitude.
     - **Homogeneous vs. inhomogeneous** fields; conductor boundary facts (perpendicular $\vec{E}$, interior field-free).     - **Homogeneous vs. inhomogeneous** fields; conductor boundary facts (perpendicular $\vec{E}$, interior field-free).
-  - Guided simulations (20–25 min) +  - Guided simulation (20–25 min) 
-  - Practice (10–15 min): +    - Place single and multiple charges; measure $\vec{E}$ at points. 
-    - Short worksheet: sketch field lines for two like charges and a dipole; compute $|\vec{E}|$ at a marked point.+  - Practice (10–15 min) 
 +    - net field on-axis of two charges; quick peer check.
   - Wrap-up (5 min):   - Wrap-up (5 min):
-    - Summary map: charges → $\vec{E}$ → $\vec{F}$; key properties and units; preview link to **equipotentials** and energy (next block).+    - Summary map: charges → $\vec{E}$ → $\vec{F}$; key properties and units.
  
-===== Conceptual overview =====+==== 9.0.4 Conceptual overview ====
 <callout icon="fa fa-lightbulb-o" color="blue"> <callout icon="fa fa-lightbulb-o" color="blue">
   - **Fields separate cause and effect**: charges set up a state in space (the field) that exists whether or not a test charge is present.   - **Fields separate cause and effect**: charges set up a state in space (the field) that exists whether or not a test charge is present.
 +  - **Coulomb field of a point charge:** $\displaystyle \vec{E}(\vec{r})=\frac{1}{4\pi\varepsilon}\frac{Q}{r^2}\,\vec{e}_{\rm r}$ (radial; outward for $Q>0$, inward for $Q<0$). Magnitude $|\vec{E}|$ follows the inverse-square law.
   - The **electric field** is a **vector field** $\vec{E}(\vec{x})$; its **direction** is the direction of the force on a *positive* test charge; its **magnitude** is given by the actinv force and the charge with units $1~{\rm N/C}=1~{\rm V/m}$.   - The **electric field** is a **vector field** $\vec{E}(\vec{x})$; its **direction** is the direction of the force on a *positive* test charge; its **magnitude** is given by the actinv force and the charge with units $1~{\rm N/C}=1~{\rm V/m}$.
   - **Point charge** model: inverse-square law; direction is radial, outward for $Q>0$, inward for $Q<0$.   - **Point charge** model: inverse-square law; direction is radial, outward for $Q>0$, inward for $Q<0$.
   - **Superposition** holds: for multiple sources, $\vec{E}_{\rm total}=\sum_k \vec{E}_k$ (vector sum at the same point).   - **Superposition** holds: for multiple sources, $\vec{E}_{\rm total}=\sum_k \vec{E}_k$ (vector sum at the same point).
-  - **Field lines** visualize $\vec{E}$: start at $+$, end at $-$, never intersect; higher line density ⇔ larger $|\vec{E}|$; lines are **not** particle trajectories. 
-  - **Homogeneous fields** (ideal between large parallel plates): parallel, equally spaced lines; **inhomogeneous fields** elsewhere (e.g., point charges, edges). 
-  - **Conductors (electrostatics)**: $\vec{E}$ is perpendicular to the surface; interior is field-free; surface charge arranges to enforce these conditions. 
 </callout> </callout>
  
 ~~PAGEBREAK~~ ~~CLEARFIX~~ ~~PAGEBREAK~~ ~~CLEARFIX~~
  
-===== Core content =====+===== 9.1 Core content =====
  
-==== Electric Effects ====+==== 9.1.1 Electric Effects ====
  
 Every day life teaches us that there are various charges and their effects. The image <imgref ImgNr01> depicts a chargeable body that can be charged through charge separation between the sole and the floor. The movement of the foot generates a negative surplus charge in the body, which progressively spreads throughout the body. A current can flow even through the air if a pointed portion of the body (e.g., a finger) is brought into close proximity to a charge reservoir with no extra charges. Every day life teaches us that there are various charges and their effects. The image <imgref ImgNr01> depicts a chargeable body that can be charged through charge separation between the sole and the floor. The movement of the foot generates a negative surplus charge in the body, which progressively spreads throughout the body. A current can flow even through the air if a pointed portion of the body (e.g., a finger) is brought into close proximity to a charge reservoir with no extra charges.
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 Furthermore, electrodynamics is not covered in this chapter and is provided in further detail in subsequent chapters. Furthermore, electrodynamics is not covered in this chapter and is provided in further detail in subsequent chapters.
  
-==== Fields ====+==== 9.1.2 Fields ====
  
 The concept of a field will now be briefly discussed in more detail. The concept of a field will now be briefly discussed in more detail.
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 </callout> </callout>
  
-==== The electric Field ====+==== 9.1.3 The electric Field ====
  
 We had already considered the charge as the central quantity of electricity in [[block02]] and recognized it as a multiple of the elementary charge.  We had already considered the charge as the central quantity of electricity in [[block02]] and recognized it as a multiple of the elementary charge. 
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-==== Direction of the Coulomb force and Superposition ====+==== 9.1.4 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). 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).
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 </WRAP> </WRAP>
  
-==== Energy required to Displace a Charge in the electric Field ====+==== 9.1.5 Energy required to Displace a Charge in the electric Field ====
  
 Now we want to see, whether we can derive the required energy to displace a charge in the electric field. \\ Now we want to see, whether we can derive the required energy to displace a charge in the electric field. \\
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 ~~PAGEBREAK~~ ~~CLEARFIX~~ ~~PAGEBREAK~~ ~~CLEARFIX~~
  
-===== Common pitfalls =====+===== 9.2 Common Pitfalls =====
   * Treating **force** and **field** as the same thing; forgetting $\vec{F}=q\,\vec{E}$ and the positive-test-charge convention.   * Treating **force** and **field** as the same thing; forgetting $\vec{F}=q\,\vec{E}$ and the positive-test-charge convention.
   * Mixing units (${\rm N}$, ${\rm C}$, ${\rm V}$, ${\rm m}$): not recognizing $1~{\rm N/C}=1~{\rm V/m}$.   * Mixing units (${\rm N}$, ${\rm C}$, ${\rm V}$, ${\rm m}$): not recognizing $1~{\rm N/C}=1~{\rm V/m}$.
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   * Forgetting conductor boundary facts: lines must be **perpendicular** to ideal conducting surfaces; interior **$|\vec{E}|=0$** in electrostatics.   * Forgetting conductor boundary facts: lines must be **perpendicular** to ideal conducting surfaces; interior **$|\vec{E}|=0$** in electrostatics.
      
-===== Exercises =====+===== 9.3 Exercises =====
  
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 + 
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 <panel type="info" title="Task 1.2.4 Superposition of Charges in 1D"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%> <panel type="info" title="Task 1.2.4 Superposition of Charges in 1D"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>