Question

Точечный заряд 1 ∙ 10^-7 Кл помещён в вакууме, а точечный заряд 3 ∙ 10^-7 Кл - в некоторой жидкости. Напряженности поля в точках, равноотстоящих от зарядов, одинаковы. Определите диэлектрическую проницаемость жидкости.

Answer 1

Пусть заряд $q_1$ находится в вакууме, а заряд $q_2$ -в жидкости.

 

Тогда напряженности полей этих зарядов равны соответственно:

 

$E_1=k\frac{q_1}{r^2},\ E_2= k\frac{q_2}{\varepsilon r^2}$

 

По условию напряженности полей на одинаковых расстояния равны, значит:

 

$q_1=\frac{q_2}\varepsilon$

 

Значит

 

$\varepsilon=\frac{q_2}{q_1}=3$

 

 

Answer 2

Calculation of the Dielectric Permittivity of the Liquid

To determine the dielectric permittivity of the liquid, we can use the formula:

ε = ε₀ * (E_vacuum / E_liquid)

where: - ε is the dielectric permittivity of the liquid, - ε₀ is the vacuum permittivity (ε₀ = 8.854 x 10^-12 F/m), - E_vacuum is the electric field intensity in vacuum, - E_liquid is the electric field intensity in the liquid.

Given that the electric field intensities in the points equidistant from the charges are the same, we can equate the electric field intensities in vacuum and in the liquid:

E_vacuum = E_liquid

Now, let's calculate the dielectric permittivity of the liquid using the given values:

- Point charge 1: q₁ = 1 x 10^-7 C - Point charge 2: q₂ = 3 x 10^-7 C

Using the formula above, we can calculate the dielectric permittivity of the liquid.

Calculation:

Using the given information, we have:

- q₁ = 1 x 10^-7 C - q₂ = 3 x 10^-7 C

Let's calculate the dielectric permittivity of the liquid:

ε = ε₀ * (E_vacuum / E_liquid)

Since the electric field intensities in the points equidistant from the charges are the same, we can equate the electric field intensities in vacuum and in the liquid:

E_vacuum = E_liquid

Substituting this into the formula, we get:

ε = ε₀

Therefore, the dielectric permittivity of the liquid is equal to the vacuum permittivity (ε₀ = 8.854 x 10^-12 F/m).

Please note that the given question does not provide enough information to calculate the dielectric permittivity of the liquid. The dielectric permittivity depends on the properties of the specific liquid, which are not provided in the question.