Новое решение

Alexphysics правка от 24 июн. 2026 г., 23:59

правка #19176 позже →

en/11.3.8.md +24 −0

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		+	### Statement
		+
		+	$11.3.8.$ [Insert the problem statement]
		+
		+	### Solution
		+
		+	For two thin conducting flat plates of width d separated by a distance" h (h \ll d)$, equal and opposite currents produce a practically uniform magnetic field in the space between them. Applying Ampère's law to a rectangular path that crosses one plate, we obtain $H = I/d $and$ B = \mu_0 I/d$
		+
		+	The magnetic flux per unit length crossing the area$ h \times 1 $between the plates is
		+
		+	$ \Phi' = B h = \mu_0 I h / d$ Therefore, the inductance per unit length is:
		+
		+	$L' = \frac{\Phi'}{I} = \frac{\mu_0 h}{d}$
		+
		+	Substituting the numerical values
		+	$(h = 5\ \text{mm} = 0.005\ \text{m}, d = 0.1\ \text{m}, \mu_0 = 4\pi \times 10^{-7}\ \text{H/m})$
		+
		+	$L' = \frac{4\pi \times 10^{-7} \times 0.005}{0.1} = 2\pi \times 10^{-8}\ \text{H/m} \approx 6.28 \times 10^{-8}\ \text{H/m}$
		+
		+	$\boxed{L' \approx 6.3 \times 10^{-8}\ \text{H/m} \; (= 63\ \text{nH/m})}$
		+
		+	#### Answer
		+
		+	[Insert a concise answer or boxed result]

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			### Statement

			$11.3.8.$ [Insert the problem statement]

			### Solution

			For two thin conducting flat plates of width d separated by a distance" h (h \ll d)$, equal and opposite currents produce a practically uniform magnetic field in the space between them. Applying Ampère's law to a rectangular path that crosses one plate, we obtain $H = I/d $and$ B = \mu_0 I/d$

			The magnetic flux per unit length crossing the area$ h \times 1 $between the plates is

			$ \Phi' = B h = \mu_0 I h / d$ Therefore, the inductance per unit length is:

			$L' = \frac{\Phi'}{I} = \frac{\mu_0 h}{d}$

			Substituting the numerical values
			$(h = 5\ \text{mm} = 0.005\ \text{m}, d = 0.1\ \text{m}, \mu_0 = 4\pi \times 10^{-7}\ \text{H/m})$

			$L' = \frac{4\pi \times 10^{-7} \times 0.005}{0.1} = 2\pi \times 10^{-8}\ \text{H/m} \approx 6.28 \times 10^{-8}\ \text{H/m}$

			$\boxed{L' \approx 6.3 \times 10^{-8}\ \text{H/m} \; (= 63\ \text{nH/m})}$

			#### Answer

			[Insert a concise answer or boxed result]