Новое решение

Alexphysics правка от 25 июн. 2026 г., 12:55

правка #19208 позже →

en/11.3.12.md +22 −0

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		+	### Statement
		+
		+	$11.3.12.$ [Insert the problem statement]
		+
		+	### Solution
		+
		+	For this problem we can use scaling arguments. The inductance of a system of conductors with linear media is proportional to the characteristic length.
		+
		+	If each linear dimension is multiplied by k, the total inductance is also multiplied by k. This follows from dimensional analysis:
		+	inductance has units of
		+
		+	$\text{H} = \text{Wb/A} = \text{T·m}^2/\text{A}$
		+
		+	and since the magnetic field of a current configuration scales inversely with distance, the magnetic flux ends up being proportional to the current and to the length, so that L is proportional to length.
		+
		+	Therefore, when all linear dimensions (radii, distances between conductors, and total length of the system) are scaled by a factor k, the inductance increases by a factor of k:
		+
		+	$\boxed{L_{\text{new}} = k\,L_{\text{original}}}$.
		+
		+	#### Answer
		+
		+	[Insert a concise answer or boxed result]

	@@ -0,0 +1,22 @@
			### Statement

			$11.3.12.$ [Insert the problem statement]

			### Solution

			For this problem we can use scaling arguments. The inductance of a system of conductors with linear media is proportional to the characteristic length.

			If each linear dimension is multiplied by k, the total inductance is also multiplied by k. This follows from dimensional analysis:
			inductance has units of

			$\text{H} = \text{Wb/A} = \text{T·m}^2/\text{A}$

			and since the magnetic field of a current configuration scales inversely with distance, the magnetic flux ends up being proportional to the current and to the length, so that L is proportional to length.

			Therefore, when all linear dimensions (radii, distances between conductors, and total length of the system) are scaled by a factor k, the inductance increases by a factor of k:

			$\boxed{L_{\text{new}} = k\,L_{\text{original}}}$.

			#### Answer

			[Insert a concise answer or boxed result]