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electrical_engineering_and_electronics_1:block09 [2025/10/27 00:53] – mexleadminelectrical_engineering_and_electronics_1:block09 [2025/11/01 00:14] (aktuell) – [Block 09 - Force on charges and electric field strength] mexleadmin
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-====== Block 09 - Force on charges and electric field strength ======+====== Block 09 - Force on Charges and electric Field Strength ======
  
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 <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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 +~~PAGEBREAK~~ ~~CLEARFIX~~
 +===== 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~~
 ===== 90-minute plan ===== ===== 90-minute plan =====
   - Warm-up (8–10 min):   - Warm-up (8–10 min):
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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 ===== ===== 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. 
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 ===== Embedded resources ===== ===== Embedded resources =====