Edits to “Statement”, “Solution and Answer”

Valter edited Aug 25, 2026, 7:05 PM

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revision #20326 parent #20325 ← older

en/6.4.1.md +2 −10

		@@ -1,11 +1,5 @@
			### Statement

		−	$6.4.1.$ [Insert the problem statement]
		−
		−	### Solution
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		−	### Statement
		−
			$6.4.1.$ What is an electrical capacitor? What is the capacitance of a capacitor? How does the definition of the capacitance of an isolated conductor differ from the definition of the capacitance of a capacitor?

			### Solution and Answer

			An <b>electrical capacitor</b> is a device consisting of two conductors (plates) separated by a dielectric, designed to accumulate electric charge and electric field energy.

		@@ -15,11 +9,13 @@Solution and Answer
			The <b>capacitance of a capacitor</b> ($C$) is a physical quantity characterizing the ability of a capacitor to accumulate charge at a given voltage between its plates. It is defined as the ratio of the charge ($Q$) on one of the plates to the voltage ($U$) between them: $C = Q/U$. The SI unit of capacitance is the farad (F).

			<b>Isolated conductor:</b>
		+
			This is a single conductor located far from other charged bodies.
			Its capacitance is defined as the ratio of the charge ($Q$) on the conductor to its potential ($\phi$): $C = Q/\phi$.
			The potential depends only on the charge and the geometry of the conductor (for example, a sphere of radius $R$ has a capacitance $C = 4\pi\varepsilon_0 R$).

			<b>Capacitor:</b>
		+
			Consists of two conductors (plates) with charges equal in magnitude but opposite in sign.
			Capacitance is defined as the ratio of the charge ($Q$) on one plate to the potential difference ($U$) between the plates: $C = Q/U$.
			It depends on the geometry of the plates, the distance between them, and the properties of the dielectric.

			An isolated conductor has capacitance relative to infinity (the potential is measured from zero at infinity).

		@@ -29,7 +25,3 @@Solution and Answer
			A capacitor is characterized by the capacitance between two conductors, and its capacitance is usually much larger than that of an isolated conductor of comparable size.

			The capacitance of a capacitor is defined through the potential difference between the plates, while the capacitance of an isolated conductor is defined through its own potential relative to infinity.
		−
		−	#### Answer
		−
		−	[Insert a concise answer or boxed result]

	@@ -1,11 +1,5 @@
	### Statement		### Statement

	$6.4.1.$ [Insert the problem statement]

	### Solution

	### Statement

	$6.4.1.$ What is an electrical capacitor? What is the capacitance of a capacitor? How does the definition of the capacitance of an isolated conductor differ from the definition of the capacitance of a capacitor?		$6.4.1.$ What is an electrical capacitor? What is the capacitance of a capacitor? How does the definition of the capacitance of an isolated conductor differ from the definition of the capacitance of a capacitor?

	### Solution and Answer		### Solution and Answer

	An <b>electrical capacitor</b> is a device consisting of two conductors (plates) separated by a dielectric, designed to accumulate electric charge and electric field energy.		An <b>electrical capacitor</b> is a device consisting of two conductors (plates) separated by a dielectric, designed to accumulate electric charge and electric field energy.

	@@ -15,11 +9,13 @@Solution and Answer
	The <b>capacitance of a capacitor</b> ($C$) is a physical quantity characterizing the ability of a capacitor to accumulate charge at a given voltage between its plates. It is defined as the ratio of the charge ($Q$) on one of the plates to the voltage ($U$) between them: $C = Q/U$. The SI unit of capacitance is the farad (F).		The <b>capacitance of a capacitor</b> ($C$) is a physical quantity characterizing the ability of a capacitor to accumulate charge at a given voltage between its plates. It is defined as the ratio of the charge ($Q$) on one of the plates to the voltage ($U$) between them: $C = Q/U$. The SI unit of capacitance is the farad (F).

	<b>Isolated conductor:</b>		<b>Isolated conductor:</b>

	This is a single conductor located far from other charged bodies.		This is a single conductor located far from other charged bodies.
	Its capacitance is defined as the ratio of the charge ($Q$) on the conductor to its potential ($\phi$): $C = Q/\phi$.		Its capacitance is defined as the ratio of the charge ($Q$) on the conductor to its potential ($\phi$): $C = Q/\phi$.
	The potential depends only on the charge and the geometry of the conductor (for example, a sphere of radius $R$ has a capacitance $C = 4\pi\varepsilon_0 R$).		The potential depends only on the charge and the geometry of the conductor (for example, a sphere of radius $R$ has a capacitance $C = 4\pi\varepsilon_0 R$).

	<b>Capacitor:</b>		<b>Capacitor:</b>

	Consists of two conductors (plates) with charges equal in magnitude but opposite in sign.		Consists of two conductors (plates) with charges equal in magnitude but opposite in sign.
	Capacitance is defined as the ratio of the charge ($Q$) on one plate to the potential difference ($U$) between the plates: $C = Q/U$.		Capacitance is defined as the ratio of the charge ($Q$) on one plate to the potential difference ($U$) between the plates: $C = Q/U$.
	It depends on the geometry of the plates, the distance between them, and the properties of the dielectric.		It depends on the geometry of the plates, the distance between them, and the properties of the dielectric.

	An isolated conductor has capacitance relative to infinity (the potential is measured from zero at infinity).		An isolated conductor has capacitance relative to infinity (the potential is measured from zero at infinity).

	@@ -29,7 +25,3 @@Solution and Answer
	A capacitor is characterized by the capacitance between two conductors, and its capacitance is usually much larger than that of an isolated conductor of comparable size.		A capacitor is characterized by the capacitance between two conductors, and its capacitance is usually much larger than that of an isolated conductor of comparable size.

	The capacitance of a capacitor is defined through the potential difference between the plates, while the capacitance of an isolated conductor is defined through its own potential relative to infinity.		The capacitance of a capacitor is defined through the potential difference between the plates, while the capacitance of an isolated conductor is defined through its own potential relative to infinity.

	#### Answer

	[Insert a concise answer or boxed result]