Новое решение
en/11.5.27.md
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| + | ### Statement | ||
| + | |||
| + | $11.5.27.$ [Insert the problem statement] | ||
| + | |||
| + | ### Solution | ||
| + | |||
| + | Before equilibrium is established, the flow changes according to the following law: | ||
| + | $$\frac{d\Phi}{d t} =\frac{d(B - B_e)}{dt} \pi r^2$$ | ||
| + | Where $B_e$ is the interference generated by the motion of electrons. | ||
| + | The vortex electric field is determined by the circulation theorem: | ||
| + | $$E 2\pi r = \frac{d(B - B_e)}{dt} \pi r^2$$ | ||
| + | $$E = \frac{d(B - B_e)}{dt} \frac{r}{2}$$ | ||
| + | Let's write 2nd law: | ||
| + | $$m\frac{d \upsilon}{dt} = \frac{d(B - B_e)}{dt} \frac{re}{2}$$ | ||
| + | From here: | ||
| + | $$\upsilon = (B - B_e) \frac{re}{2m}$$ | ||
| + | Let's find the current density: | ||
| + | $$j = \frac{n_e \upsilon dt Lh e}{Lh dt}$$ | ||
| + | $$j = n_e \upsilon e$$ | ||
| + | The equivalent linear current density is: | ||
| + | $$i = n_e \upsilon e h$$ | ||
| + | Therefore: | ||
| + | $$B_e = \mu_0 n_e \upsilon e h$$ | ||
| + | Substitute the velocity and find $B_e$: | ||
| + | $$B_e = \frac{B}{1 + \frac{2m}{\mu_0 n_e e^2 h r}}$$ | ||
| + | From here, the desired induction inside: | ||
| + | $$B' = B - B_e = \frac{Bm}{m + \frac{\mu_0 n_e e^2 h r}{2}} \approx 5.7 \cdot 10^{-5} Т$$ | ||
| + | |||
| + | #### Answer | ||
| + | |||
| + | [Insert a concise answer or boxed result] | ||
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| ### Statement | |||
| $11.5.27.$ [Insert the problem statement] | |||
| ### Solution | |||
| Before equilibrium is established, the flow changes according to the following law: | |||
| $$\frac{d\Phi}{d t} =\frac{d(B - B_e)}{dt} \pi r^2$$ | |||
| Where $B_e$ is the interference generated by the motion of electrons. | |||
| The vortex electric field is determined by the circulation theorem: | |||
| $$E 2\pi r = \frac{d(B - B_e)}{dt} \pi r^2$$ | |||
| $$E = \frac{d(B - B_e)}{dt} \frac{r}{2}$$ | |||
| Let's write 2nd law: | |||
| $$m\frac{d \upsilon}{dt} = \frac{d(B - B_e)}{dt} \frac{re}{2}$$ | |||
| From here: | |||
| $$\upsilon = (B - B_e) \frac{re}{2m}$$ | |||
| Let's find the current density: | |||
| $$j = \frac{n_e \upsilon dt Lh e}{Lh dt}$$ | |||
| $$j = n_e \upsilon e$$ | |||
| The equivalent linear current density is: | |||
| $$i = n_e \upsilon e h$$ | |||
| Therefore: | |||
| $$B_e = \mu_0 n_e \upsilon e h$$ | |||
| Substitute the velocity and find $B_e$: | |||
| $$B_e = \frac{B}{1 + \frac{2m}{\mu_0 n_e e^2 h r}}$$ | |||
| From here, the desired induction inside: | |||
| $$B' = B - B_e = \frac{Bm}{m + \frac{\mu_0 n_e e^2 h r}{2}} \approx 5.7 \cdot 10^{-5} Т$$ | |||
| #### Answer | |||
| [Insert a concise answer or boxed result] | |||