Question

Определите диэлектрическую проницаемость вещества, в котором на расстоянии r=0,12 м. друг от друга находятся два точечных заряда q1=8нКл и q2=16нКл, если модуль силы их электростатического взаимодействия F=20мкН

Answer 1

F = k/e *q1*q2/r^2

e= k/F *q1*q2/r^2 = 9*10^9 /(20*10^-6)*8*10^-9*16*10^-9 / 0.12^2 =4

ОТВЕТ 4

Answer 2

$F=k*|q1|*|q2|/(r^2*e)$

 

Где e=ε (эпсилон) - искомая диэлектрическая проницаемость, F - сила Кулона, |q1| и |q2| - модули зарядов, r - расстояние между зарядами.

 

Выразим отсюда ε:

 

$e=k*|q1|*|q2|/(F*r^2)$

 

Итак, ε=4

Answer 3

Calculation of the Dielectric Permittivity

To determine the dielectric permittivity of the substance, we can use the formula for the electric field between two point charges:

\[E = \frac{{k \cdot q_1}}{{r^2}} + \frac{{-k \cdot q_2}}{{(l + r)^2}}\]

Where: - \(E\) is the electric field between the charges, - \(k\) is the Coulomb constant (\(9 \times 10^9 \, \text{N} \cdot \text{m}^2/\text{C}^2\)), - \(q_1\) and \(q_2\) are the magnitudes of the charges (\(8 \, \text{nC}\) and \(16 \, \text{nC}\) respectively), - \(r\) is the distance between the charges (\(0.12 \, \text{m}\)), - \(l\) is the distance between the charges and the substance.

We are given that the magnitude of the electric field is \(20 \, \text{μN}\) (\(20 \times 10^{-6} \, \text{N}\)). We can set up the equation as follows:

\[20 \times 10^{-6} = \frac{{(9 \times 10^9 \cdot 8 \times 10^{-9})}}{{(0.12)^2}} + \frac{{-(9 \times 10^9 \cdot 16 \times 10^{-9})}}{{(l + 0.12)^2}}\]

Simplifying the equation, we get:

\[20 \times 10^{-6} = \frac{{9 \times 8}}{{(0.12)^2}} - \frac{{9 \times 16}}{{(l + 0.12)^2}}\]

Solving for \(l\), we find:

\[l = \sqrt{\frac{{9 \times 16}}{{(20 \times 10^{-6} - 9 \times 8/(0.12)^2)}}} - 0.12\]

Evaluating this expression, we find that \(l \approx 0.06 \, \text{m}\).

Now, we can substitute the value of \(l\) into the equation for the electric field to find the dielectric permittivity:

\[E = \frac{{k \cdot q_1}}{{r^2}} + \frac{{-k \cdot q_2}}{{(l + r)^2}}\]

Substituting the given values, we have:

\[E = \frac{{9 \times 10^9 \cdot 8 \times 10^{-9}}}{{(0.12)^2}} + \frac{{-9 \times 10^9 \cdot 16 \times 10^{-9}}}{{(0.06 + 0.12)^2}}\]

Simplifying the equation, we find:

\[E \approx 37.5 \, \text{N/C}\]

Therefore, the dielectric permittivity of the substance is approximately 37.5.