Unterschiede
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| Beide Seiten der vorigen Revision Vorhergehende Überarbeitung Nächste Überarbeitung | Vorhergehende Überarbeitung | ||
| electrical_engineering_and_electronics_1:block16 [2025/11/23 02:08] – mexleadmin | electrical_engineering_and_electronics_1:block16 [2026/01/10 12:46] (aktuell) – mexleadmin | ||
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| Zeile 1: | Zeile 1: | ||
| ====== Block 16 - Ampère' | ====== Block 16 - Ampère' | ||
| - | ===== Learning objectives | + | ===== 16.0 Intro ===== |
| + | |||
| + | ==== 16.0.1 | ||
| < | < | ||
| After this 90-minute block, you can | After this 90-minute block, you can | ||
| Zeile 7: | Zeile 9: | ||
| </ | </ | ||
| - | ===== Preparation at Home ===== | + | ==== 16.0.2 |
| Well, again | Well, again | ||
| Zeile 16: | Zeile 18: | ||
| * ... | * ... | ||
| - | ===== 90-minute plan ===== | + | ==== 16.0.3 |
| - Warm-up (x min): | - Warm-up (x min): | ||
| - .... | - .... | ||
| Zeile 24: | Zeile 26: | ||
| - Wrap-up (x min): Summary box; common pitfalls checklist. | - Wrap-up (x min): Summary box; common pitfalls checklist. | ||
| - | ===== Conceptual overview | + | ==== 16.0.4 |
| <callout icon=" | <callout icon=" | ||
| - ... | - ... | ||
| </ | </ | ||
| - | ===== Core content ===== | + | ===== 16.1 Core content ===== |
| - | ===== Generalization of the Magnetic Field Strength | + | ==== 16.1.1 |
| - | So far, only the rotational symmetric problem | + | So far, only the rotational symmetric problem |
| \begin{align*} | \begin{align*} | ||
| Zeile 43: | Zeile 45: | ||
| \begin{align*} | \begin{align*} | ||
| - | U = E \cdot s \quad \quad | \quad \text{applies to capacitor only} | + | U = E \cdot s \quad \quad | \quad \text{applies to plate capacitor only} |
| \end{align*} | \end{align*} | ||
| Zeile 103: | Zeile 105: | ||
| </ | </ | ||
| + | ~~PAGEBREAK~~ ~~CLEARFIX~~ | ||
| + | ==== 16.1.2 | ||
| + | <WRAP group>< | ||
| + | === longitudinal coil === | ||
| + | < | ||
| + | < | ||
| + | {{url> | ||
| + | </ | ||
| + | A longitudinal coil can be seen in <imgref BildNr04> | ||
| + | |||
| + | The created field density of the coil can be derived from Ampere' | ||
| + | |||
| + | \begin{align*} | ||
| + | \theta(t) &= \int & \vec{H}(t) \cdot {\rm d}\vec{s} \\ | ||
| + | &= \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} | ||
| + | & | ||
| + | \end{align*} | ||
| + | |||
| + | The magnetic field in a toroidal coil is often considered as homogenious in the inner volume, when the length $l$ is much larger than the diameter: $l \gg d$. \\ | ||
| + | With a given number $N$ of windings, the magnetic field strength $H$ is | ||
| + | |||
| + | \begin{align*} | ||
| + | \theta = H \cdot l = N \cdot I | ||
| + | \end{align*} | ||
| + | \begin{align*} | ||
| + | \boxed{H = {{N \cdot I}\over{l}}} | ||
| + | \end{align*} | ||
| + | |||
| + | </ | ||
| + | === toroidal coil === | ||
| + | < | ||
| + | < | ||
| + | {{url> | ||
| + | </ | ||
| + | |||
| + | A toroidal coil has a donut-like setup. This can be seen in <imgref BildNr05> | ||
| + | The toroidal coil is often defined by: | ||
| + | * The minor radius $r$: The radius | ||
| + | * The major radius $R$: The distance from the center of the entire toroid (the center of the hole) to the center of the circular cross-section of the coil. | ||
| + | For reasons of symmetry, it shall get clear that the field lines form concentric circles. \\ | ||
| + | Also the magnetic field strength $H$ in a toroidal coil is often considered as homogenious, | ||
| + | |||
| + | \begin{align*} | ||
| + | \theta = H \cdot 2\pi R = N \cdot I | ||
| + | \end{align*} | ||
| + | \begin{align*} | ||
| + | \boxed{H = {{N \cdot I}\over{2\pi R}}} \biggr | _\text{toroidal coil} | ||
| + | \end{align*} | ||
| + | </ | ||
| - | ===== Common pitfalls ===== | + | ===== 16.2 Common pitfalls ===== |
| * ... | * ... | ||
| - | ===== Exercises ===== | + | ===== 16.3 Exercises ===== |
| <panel type=" | <panel type=" | ||