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		+	### Statement
		+
		+	$6.6.1.$ [Insert the problem statement]
		+
		+	### Solution
		+
		+	### Statement
		+
		+	$6.6.1.$
		+	a. What explains the decrease in the electric field strength in a substance?
		+	b. What is the permittivity (dielectric constant) of a substance?
		+	c. How does the permittivity of a gas depend on its pressure?
		+
		+	### Solution
		+
		+	<b>a.</b> The decrease in the electric field strength in a substance is explained by the <b>polarization of the dielectric</b>.
		+	When a dielectric is placed in an external electric field $\vec{E}_0$, the electric charges within its atoms and molecules shift (or the existing dipoles align). As a result, uncompensated macroscopic <b>bound (polarization) charges</b> appear on the surfaces of the dielectric.
		+	These charges create their own internal electric field $\vec{E}_{\text{pol}}$, which is directed opposite to the external field. According to the superposition principle, the resulting field $\vec{E}$ inside the substance is:
		+	$$\vec{E} = \vec{E}_0 + \vec{E}_{\text{pol}}$$
		+	In scalar form (for magnitudes, since they are directed oppositely):
		+	$$E = E_0 - E_{\text{pol}}$$
		+	Consequently, the resulting field inside the dielectric is weaker than the external one.
		+
		+	<b>b.</b> <b>Permittivity</b> (or relative dielectric constant, $\varepsilon$) is a dimensionless physical quantity that shows how many times the magnitude of the electric field $E$ inside a homogeneous isotropic dielectric is less than the magnitude of the external field $E_0$ (in a vacuum):
		+	$$\varepsilon = \frac{E_0}{E}$$
		+	For vacuum, $\varepsilon = 1$; for all dielectrics, $\varepsilon > 1$.
		+
		+	<b>c.</b> For gases, the difference $(\varepsilon - 1)$ is directly proportional to the molecular concentration $n$:
		+	$$\varepsilon - 1 \sim n$$
		+	From the ideal gas equation of state, at a constant temperature ($T = \text{const}$), the concentration of molecules is directly proportional to the pressure: $n = \frac{P}{kT} \implies n \sim P$.
		+	Therefore:
		+	$$\varepsilon - 1 \sim P$$
		+	Thus, as the pressure increases, the permittivity of the gas increases, with the quantity $(\varepsilon - 1)$ growing linearly.
		+
		+	#### Answer
		+	a. By the polarization of the dielectric (the emergence of bound charges creating an opposing field).
		+	b. A quantity indicating how many times the field strength in a substance is less than in a vacuum ($\varepsilon = E_0 / E$).
		+	c. Permittivity increases with pressure (the quantity $\varepsilon - 1$ is directly proportional to the pressure).
		+
		+	#### Answer
		+
		+	[Insert a concise answer or boxed result]

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			### Statement

			$6.6.1.$ [Insert the problem statement]

			### Solution

			### Statement

			$6.6.1.$
			a. What explains the decrease in the electric field strength in a substance?
			b. What is the permittivity (dielectric constant) of a substance?
			c. How does the permittivity of a gas depend on its pressure?

			### Solution

			<b>a.</b> The decrease in the electric field strength in a substance is explained by the <b>polarization of the dielectric</b>.
			When a dielectric is placed in an external electric field $\vec{E}_0$, the electric charges within its atoms and molecules shift (or the existing dipoles align). As a result, uncompensated macroscopic <b>bound (polarization) charges</b> appear on the surfaces of the dielectric.
			These charges create their own internal electric field $\vec{E}_{\text{pol}}$, which is directed opposite to the external field. According to the superposition principle, the resulting field $\vec{E}$ inside the substance is:
			$$\vec{E} = \vec{E}_0 + \vec{E}_{\text{pol}}$$
			In scalar form (for magnitudes, since they are directed oppositely):
			$$E = E_0 - E_{\text{pol}}$$
			Consequently, the resulting field inside the dielectric is weaker than the external one.

			<b>b.</b> <b>Permittivity</b> (or relative dielectric constant, $\varepsilon$) is a dimensionless physical quantity that shows how many times the magnitude of the electric field $E$ inside a homogeneous isotropic dielectric is less than the magnitude of the external field $E_0$ (in a vacuum):
			$$\varepsilon = \frac{E_0}{E}$$
			For vacuum, $\varepsilon = 1$; for all dielectrics, $\varepsilon > 1$.

			<b>c.</b> For gases, the difference $(\varepsilon - 1)$ is directly proportional to the molecular concentration $n$:
			$$\varepsilon - 1 \sim n$$
			From the ideal gas equation of state, at a constant temperature ($T = \text{const}$), the concentration of molecules is directly proportional to the pressure: $n = \frac{P}{kT} \implies n \sim P$.
			Therefore:
			$$\varepsilon - 1 \sim P$$
			Thus, as the pressure increases, the permittivity of the gas increases, with the quantity $(\varepsilon - 1)$ growing linearly.

			#### Answer
			a. By the polarization of the dielectric (the emergence of bound charges creating an opposing field).
			b. A quantity indicating how many times the field strength in a substance is less than in a vacuum ($\varepsilon = E_0 / E$).
			c. Permittivity increases with pressure (the quantity $\varepsilon - 1$ is directly proportional to the pressure).

			#### Answer

			[Insert a concise answer or boxed result]