Правка разделов «Statement», «Solution»

Alexphysics правка от 28 июн. 2026 г., 16:55

правка #19339 предыдущая #19338 ← раньше позже →

en/12.1.17.md +9 −5

		@@ -1,7 +1,15 @@
			### Statement

		−	$12.1.17.$ ~~[Insert the problem statement]~~
		+	$12.1.17.$

		+	The thicker the film, the greater the amplitude of the electric field strength of
		+	an electromagnetic wave reflected from a conductive film. The figure shows a
		+	typical dependence of the reflected wave amplitude on the film thickness. At
		+	the initial moment (in the region x < x1), the amplitude linearly depends on
		+	the film thickness x, then the linear dependence is broken, and in the region
		+	x > x2, the amplitude of the reflected wave differs little from the amplitude of
		+	the incident wave E0. Explain this dependency.
		+
			### Solution

			The behavior is explained by the interaction of the electromagnetic wave with the free electrons of the material.

			For very small thicknesses (x < x_1), the film is semi-transparent. The incident wave penetrates completely and sets all the free electrons of the film into motion. The induced current, and therefore the re-emitted field (reflected wave), is proportional to the number of electrons and, consequently, to the thickness x. Hence, the reflected amplitude grows linearly with x.

		@@ -11,7 +19,3 @@Solution
			As the thickness increases (x_1 < x < x_2), it reaches a dimension comparable to the penetration depth (or skin depth) of the material at that frequency. The incident wave no longer manages to pass completely through the film; the induced current stops growing proportionally because the deeper layers contribute less and less. The growth of the reflected amplitude slows down, and the dependence is no longer linear.

			When the thickness greatly exceeds the penetration depth (x > x_2), the film behaves like a bulk conductor. The incident wave is almost completely attenuated before reaching the back face. All the non-dissipated energy is re-emitted backward, and the amplitude of the reflected wave asymptotically approaches the incident amplitude$ E_0$ Beyond this point, increasing the thickness practically does not change the reflection.
		−
		−	#### Answer
		−
		−	[Insert a concise answer or boxed result]

	@@ -1,7 +1,15 @@
	### Statement		### Statement

	$12.1.17.$ ~~[Insert the problem statement]~~		$12.1.17.$

			The thicker the film, the greater the amplitude of the electric field strength of
			an electromagnetic wave reflected from a conductive film. The figure shows a
			typical dependence of the reflected wave amplitude on the film thickness. At
			the initial moment (in the region x < x1), the amplitude linearly depends on
			the film thickness x, then the linear dependence is broken, and in the region
			x > x2, the amplitude of the reflected wave differs little from the amplitude of
			the incident wave E0. Explain this dependency.

	### Solution		### Solution

	The behavior is explained by the interaction of the electromagnetic wave with the free electrons of the material.		The behavior is explained by the interaction of the electromagnetic wave with the free electrons of the material.

	For very small thicknesses (x < x_1), the film is semi-transparent. The incident wave penetrates completely and sets all the free electrons of the film into motion. The induced current, and therefore the re-emitted field (reflected wave), is proportional to the number of electrons and, consequently, to the thickness x. Hence, the reflected amplitude grows linearly with x.		For very small thicknesses (x < x_1), the film is semi-transparent. The incident wave penetrates completely and sets all the free electrons of the film into motion. The induced current, and therefore the re-emitted field (reflected wave), is proportional to the number of electrons and, consequently, to the thickness x. Hence, the reflected amplitude grows linearly with x.

	@@ -11,7 +19,3 @@Solution
	As the thickness increases (x_1 < x < x_2), it reaches a dimension comparable to the penetration depth (or skin depth) of the material at that frequency. The incident wave no longer manages to pass completely through the film; the induced current stops growing proportionally because the deeper layers contribute less and less. The growth of the reflected amplitude slows down, and the dependence is no longer linear.		As the thickness increases (x_1 < x < x_2), it reaches a dimension comparable to the penetration depth (or skin depth) of the material at that frequency. The incident wave no longer manages to pass completely through the film; the induced current stops growing proportionally because the deeper layers contribute less and less. The growth of the reflected amplitude slows down, and the dependence is no longer linear.

	When the thickness greatly exceeds the penetration depth (x > x_2), the film behaves like a bulk conductor. The incident wave is almost completely attenuated before reaching the back face. All the non-dissipated energy is re-emitted backward, and the amplitude of the reflected wave asymptotically approaches the incident amplitude$ E_0$ Beyond this point, increasing the thickness practically does not change the reflection.		When the thickness greatly exceeds the penetration depth (x > x_2), the film behaves like a bulk conductor. The incident wave is almost completely attenuated before reaching the back face. All the non-dissipated energy is re-emitted backward, and the amplitude of the reflected wave asymptotically approaches the incident amplitude$ E_0$ Beyond this point, increasing the thickness practically does not change the reflection.

	#### Answer

	[Insert a concise answer or boxed result]