Question

70 баллов. Точечные заряды 2 нКл и 4 нКл закреплены на расстоянии 20 см друг от друга в вакууме. На прямой, соединяющей эти заряды, на одинаковом расстоянии от каждого из них помещен третий заряд -3 нКл. Каковы модуль и направление силы, действующей на заряд?

Answer 1

Відповідь:

Модуль силы, действующей на третий заряд, равен 5,4 мкН.

Эта сила напрапвлена  в сторону заряда q₁=2 нКл.

Пояснення:

  Закон Кулона:

два точечных заряда действуют друг на друга с силой, которая обратно пропорциональна квадрату расстояния между ними и прямо пропорциональна произведению их зарядов (без учета знака зарядов) , то есть

$F_{k} =k\frac{|q_{1}| |q_{2}| }{r^{2} }$, где к=9·10⁹ Н·м²/Кл² .

   На заряд q₃ со стороны заряда q₁ действует сила притяжения, которая направлена влево (рис.) и равна:

$F_{13} =k|q_{1} ||q_{3}|/r^{2}$=9·10⁹·2·10⁻⁹·3·10⁻⁹/0,1²=5,4·10⁻⁶ H=5,4 мкН.

На заряд q₃ со стороны заряда q₂ действует сила притяжения, которая направлена вправо (рис.) и равна:

$F_{23} =k|q_{2} ||q_{3}|/r^{2}$=9·10⁹·4·10⁻⁹·3·10⁻⁹/0,1²=10,8·10⁻⁶ H=10,8 мкН.

Результирующая сила F (рис.) , действующая на заряд q₃, направлена вправо ( в сторону заряда q₂)   и равна

F = F₂₃ - F₁₃ = 10,8 - 5,4 = 5,4 мкН.

Answer 2

Calculating the Force on a Charge

To calculate the force acting on a charge, we can use Coulomb's law, which states that the magnitude of the force between two point charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between their centers. The formula for Coulomb's law is:

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

Where: - F is the magnitude of the force between the charges. - k is Coulomb's constant, approximately equal to 8.99 x 10^9 N m^2/C^2. - q1 and q2 are the magnitudes of the two charges. - r is the distance between the charges.

Applying Coulomb's Law to the Given Scenario

In the given scenario, we have two point charges, 2 nC and 4 nC, separated by a distance of 20 cm in a vacuum. A third charge of -3 nC is placed equidistant from each of the other charges on the line joining them.

Using Coulomb's law, we can calculate the force acting on the third charge (-3 nC) due to the other two charges.

First, we need to calculate the distance between the third charge and each of the other charges. Since the third charge is equidistant from the other two, we can consider the distance to be half the distance between the two original charges, i.e., 10 cm.

Now, we can calculate the force using the formula:

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

Where: - k is Coulomb's constant, approximately equal to 8.99 x 10^9 N m^2/C^2. - q1 and q2 are the magnitudes of the two charges. - r is the distance between the charges.

Calculating the Force

Using the given charges and distance, we can calculate the force acting on the third charge (-3 nC) due to the other two charges.

Let's calculate the force using the given values and Coulomb's law:

F = (8.99 x 10^9) * |(-3 x 10^-9) * (2 x 10^-9)| / (0.1)^2

F = (8.99 x 10^9) * |(-6 x 10^-18)| / 0.01

F ≈ 53.94 x 10^-9 N

The direction of the force can be determined using the principle of attraction and repulsion based on the signs of the charges involved.

Therefore, the magnitude of the force acting on the -3 nC charge is approximately 53.94 x 10^-9 N. The direction of the force will depend on the signs of the charges involved.

I hope this helps! If you have further questions, feel free to ask.