Правка разделов «Statement», «Solution», «Answer»

naz правка от 9 июн. 2026 г., 12:07

правка #18476 предыдущая #18475 ← раньше

en/9.3.15.md +20 −7

		@@ -1,22 +1,35 @@
			### Statement

		−	~~$9.3.15.$ [Insert the problem statement]~~
		+	$9.3.15.$ The circulation of the induction of a constant magnetic field through a closed circuit in a vacuum is equal
		+	to the current through the surface bounded by this circuit, multiplied by $µ0$. Please provide examples
		+	that support this law. Use it to solve the following problems:

		+	a. An infinitely long straight wire of radius $r$ flows current $I$. The current is distributed evenly over the
		+	wire cross-section. Find the magnetic field induction inside and outside the wire.
		+
		+	b. A long, wide busbar with a cross dimension of a flows a current evenly distributed over the crosssection of the conductor. Current density $j$. How does the magnetic field induction depend on the distance $x$ to the median plane of the tire?
		+
		+
			### Solution

		−	а) Возьмем круглый контур радиуса $R$ при $R>r$ весь ток входит в контур:
		+	а)
		+	Let's take a circular contour of radius $R$, when $R>r$ all the current enters the contour:
			$$B\cdot 2\pi R = \mu_0 I$$
			$$B=\frac{\mu_0 I}{2\pi R}$$
		−	~~При~~ $R < r$：
		+	with $R < r$：
			$$B\cdot 2\pi R= \mu_0 I \frac{R^2}{r^2}$$
			$$B=\frac{\mu_0 I R}{2\pi r^2}$$
		−	~~б) Рассмотрим прямоугольный контур размерами~~ $L$ на $2x$, ~~при~~ $x < a/2$:
		+	b) Let's consider a rectangular contour with dimensions
		+	$L$ and $2x$, with $x < a/2$:
			$$B \cdot 2L = \mu_0 \cdot 2jxL$$
			$$B = \mu_0 jx$$
		−	~~При~~ $x >= a/2$:
		+	with $x >= a/2$:
			$$B = \frac{\mu_0ja}{2}$$
		−	У Савченко опечатка в знаке неравенства

		+	Savchenko has a typo in the inequality sign
		+
			#### Answer

		−	[Insert a concise answer or boxed result]
		+	а. $B = \frac{\mu_0Ix}{2πr^2}$, $0 < x < r$; $B = \frac{\mu_0I}{2πx}$, $x > r$.
		+
		+	b. $B =\mu_0 xj$, $x < a/2$; $B =\frac{\mu_0 aj}{2}$, $x >= a/2$.

	@@ -1,22 +1,35 @@
	### Statement		### Statement

	~~$9.3.15.$ [Insert the problem statement]~~		$9.3.15.$ The circulation of the induction of a constant magnetic field through a closed circuit in a vacuum is equal
			to the current through the surface bounded by this circuit, multiplied by $µ0$. Please provide examples
			that support this law. Use it to solve the following problems:

			a. An infinitely long straight wire of radius $r$ flows current $I$. The current is distributed evenly over the
			wire cross-section. Find the magnetic field induction inside and outside the wire.

			b. A long, wide busbar with a cross dimension of a flows a current evenly distributed over the crosssection of the conductor. Current density $j$. How does the magnetic field induction depend on the distance $x$ to the median plane of the tire?


	### Solution		### Solution

	а) Возьмем круглый контур радиуса $R$ при $R>r$ весь ток входит в контур:		а)
			Let's take a circular contour of radius $R$, when $R>r$ all the current enters the contour:
	$$B\cdot 2\pi R = \mu_0 I$$		$$B\cdot 2\pi R = \mu_0 I$$
	$$B=\frac{\mu_0 I}{2\pi R}$$		$$B=\frac{\mu_0 I}{2\pi R}$$
	~~При~~ $R < r$：		with $R < r$：
	$$B\cdot 2\pi R= \mu_0 I \frac{R^2}{r^2}$$		$$B\cdot 2\pi R= \mu_0 I \frac{R^2}{r^2}$$
	$$B=\frac{\mu_0 I R}{2\pi r^2}$$		$$B=\frac{\mu_0 I R}{2\pi r^2}$$
	~~б) Рассмотрим прямоугольный контур размерами~~ $L$ на $2x$, ~~при~~ $x < a/2$:		b) Let's consider a rectangular contour with dimensions
			$L$ and $2x$, with $x < a/2$:
	$$B \cdot 2L = \mu_0 \cdot 2jxL$$		$$B \cdot 2L = \mu_0 \cdot 2jxL$$
	$$B = \mu_0 jx$$		$$B = \mu_0 jx$$
	~~При~~ $x >= a/2$:		with $x >= a/2$:
	$$B = \frac{\mu_0ja}{2}$$		$$B = \frac{\mu_0ja}{2}$$
	У Савченко опечатка в знаке неравенства

			Savchenko has a typo in the inequality sign

	#### Answer		#### Answer

	[Insert a concise answer or boxed result]		а. $B = \frac{\mu_0Ix}{2πr^2}$, $0 < x < r$; $B = \frac{\mu_0I}{2πx}$, $x > r$.

			b. $B =\mu_0 xj$, $x < a/2$; $B =\frac{\mu_0 aj}{2}$, $x >= a/2$.