Question

Срочно Два заряженных шара сначала взаимодействуют в воздухе. Затем их переносят в другую среду с неизвестной диэлектрической проницаемостью. На расстоянии 6 см сила взаимодействия между зарядами такая же, как и в воздухе на расстоянии 12 см друг от друга. Рассчитай диэлектрическую проницаемость неизвестной среды.​

Answer 1

Ответ: 4

Объяснение: проверил в о м

Answer 2

Calculation of the Dielectric Permittivity of an Unknown Medium

To calculate the dielectric permittivity of the unknown medium, we can use the concept of Coulomb's law, which states that the force of interaction between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

Given that the force of interaction between the charges is the same at a distance of 6 cm in the unknown medium as it is at a distance of 12 cm in air, we can set up the following equation:

F₁ = F₂

Where: - F₁ is the force of interaction between the charges at a distance of 6 cm in the unknown medium. - F₂ is the force of interaction between the charges at a distance of 12 cm in air.

Since the force of interaction between two charges is given by Coulomb's law as:

F = (k * q₁ * q₂) / r²

Where: - F is the force of interaction. - k is the electrostatic constant (k = 9 x 10^9 Nm²/C²). - q₁ and q₂ are the charges of the objects. - r is the distance between the charges.

We can rewrite the equation as:

(k * q₁ * q₂) / (r₁²) = (k * q₁ * q₂) / (r₂²)

Simplifying the equation, we get:

(r₂²) = (r₁²)

Since the distance between the charges is inversely proportional to the square root of the dielectric permittivity of the medium, we can rewrite the equation as:

(ε₂) = (ε₁) * (r₁/r₂)²

Where: - ε₂ is the dielectric permittivity of the unknown medium. - ε₁ is the dielectric permittivity of air. - r₁ is the distance between the charges in the unknown medium (6 cm). - r₂ is the distance between the charges in air (12 cm).

Now, we can substitute the values into the equation to calculate the dielectric permittivity of the unknown medium.

Let's calculate it step by step:

1. Calculate the ratio of distances: (r₁/r₂)² = (6/12)² = 0.25.

2. Substitute the value of the ratio into the equation: (ε₂) = (ε₁) * 0.25.

Since the dielectric permittivity of air is approximately 1, we can calculate the dielectric permittivity of the unknown medium as:

ε₂ = 1 * 0.25 = 0.25.

Therefore, the dielectric permittivity of the unknown medium is approximately 0.25.

Please note that the actual units of the dielectric permittivity depend on the system of units used.