Unterschiede
Hier werden die Unterschiede zwischen zwei Versionen angezeigt.
| Beide Seiten der vorigen Revision Vorhergehende Überarbeitung Nächste Überarbeitung | Vorhergehende Überarbeitung | ||
| electrical_engineering_and_electronics_1:block16 [2025/11/23 12:18] – mexleadmin | electrical_engineering_and_electronics_1:block16 [2025/12/16 14:09] (aktuell) – [Recap of the fieldline images] mexleadmin | ||
|---|---|---|---|
| Zeile 114: | Zeile 114: | ||
| A longitudinal coil can be seen in <imgref BildNr04> | 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: $l \gg d$. \\ | 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 | With a given number $N$ of windings, the magnetic field strength $H$ is | ||
| Zeile 121: | Zeile 131: | ||
| \end{align*} | \end{align*} | ||
| \begin{align*} | \begin{align*} | ||
| - | \boxed{H = {{N \cdot I}\over{l}}} \quad \quad | \quad \text{longitudinal coil} | + | \boxed{H = {{N \cdot I}\over{l}}} |
| \end{align*} | \end{align*} | ||
| Zeile 136: | Zeile 146: | ||
| * 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. | * 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. \\ | 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, | + | Also the magnetic field strength $H$ in a toroidal coil is often considered as homogenious, |
| \begin{align*} | \begin{align*} | ||
| Zeile 142: | Zeile 152: | ||
| \end{align*} | \end{align*} | ||
| \begin{align*} | \begin{align*} | ||
| - | \boxed{H = {{N \cdot I}\over{2\pi R}}} \quad \quad | \quad \text{toroidal coil} | + | \boxed{H = {{N \cdot I}\over{2\pi R}}} \biggr | _\text{toroidal coil} |
| \end{align*} | \end{align*} | ||