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en/9.2.19.md
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| + | ### Statement | ||
| + | |||
| + | $9.2.19.$ [Insert the problem statement] | ||
| + | |||
| + | ### Solution | ||
| + | |||
| + |  | ||
| + | a) let current flow in each micro circuit I I = \frac{M_0}{\Delta S} $ | ||
| + | This means that at large distances we can assume that we are dealing with a frame with the same current, the magnetic moment of such a frame (assuming the distribution of contours as in the problem $9.2.18$ $): $ $ m = n \Delta Si = nm_0$$ | ||
| + | b)Find the equivalent current flowing along the edges of the plate: | ||
| + | $$MhS=IS$$ | ||
| + | $$I = Mh$$ | ||
| + | Here, the field in the center is represented as a superposition of four fields from the frame contour. A field from one frame: | ||
| + | $$dB_1 = \frac{\mu_0 Idlsin\varphi}{4\pi r^2}$$ | ||
| + | $$dB_1 = \frac{\mu_0 I\frac{a/2d\varphi}{sin^2\varphi} sin\varphi}{4\pi \frac{(a/2)^2}{sin^2\varphi}}=\frac{\mu_0 Isin\varphi d\varphi}{4\pi a/2}$$ | ||
| + | $$B_1 = 2\int_{0}^{\pi/4}\frac{\mu_0 Isin\varphi d\varphi}{4\pi a/2}$$ | ||
| + | $$B_1 = \frac{\mu_0 I}{4\pi a/2}\cdot 2 cos(\pi/4)$$ | ||
| + | From total 4: | ||
| + | $$B = 4B_1 = \frac{2\sqrt{2}\mu_0I}{\pi a}$$ | ||
| + | Substitute the expression for the current and get the answer: | ||
| + | $$M = \frac{B\pi a}{\sqrt{8}\mu_0 h}$$ | ||
| + | |||
| + | #### Answer | ||
| + | |||
| + | [Insert a concise answer or boxed result] | ||
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| ### Statement | |||
| $9.2.19.$ [Insert the problem statement] | |||
| ### Solution | |||
|  | |||
| a) let current flow in each micro circuit I I = \frac{M_0}{\Delta S} $ | |||
| This means that at large distances we can assume that we are dealing with a frame with the same current, the magnetic moment of such a frame (assuming the distribution of contours as in the problem $9.2.18$ $): $ $ m = n \Delta Si = nm_0$$ | |||
| b)Find the equivalent current flowing along the edges of the plate: | |||
| $$MhS=IS$$ | |||
| $$I = Mh$$ | |||
| Here, the field in the center is represented as a superposition of four fields from the frame contour. A field from one frame: | |||
| $$dB_1 = \frac{\mu_0 Idlsin\varphi}{4\pi r^2}$$ | |||
| $$dB_1 = \frac{\mu_0 I\frac{a/2d\varphi}{sin^2\varphi} sin\varphi}{4\pi \frac{(a/2)^2}{sin^2\varphi}}=\frac{\mu_0 Isin\varphi d\varphi}{4\pi a/2}$$ | |||
| $$B_1 = 2\int_{0}^{\pi/4}\frac{\mu_0 Isin\varphi d\varphi}{4\pi a/2}$$ | |||
| $$B_1 = \frac{\mu_0 I}{4\pi a/2}\cdot 2 cos(\pi/4)$$ | |||
| From total 4: | |||
| $$B = 4B_1 = \frac{2\sqrt{2}\mu_0I}{\pi a}$$ | |||
| Substitute the expression for the current and get the answer: | |||
| $$M = \frac{B\pi a}{\sqrt{8}\mu_0 h}$$ | |||
| #### Answer | |||
| [Insert a concise answer or boxed result] | |||