Question

Два одинаковых металических шарика с зарядами 1 нКл и 3 нКл находятся на определенном расстоянии друг от друга. Их приводит в соприкосновение и разводят на расстояние,которое в 2 раза больше первоначального. Во сколько раз уменьшится сила взаимодействия

Answer 1

Величина зарядов после соприкосновения: q₁=q₂ =(1+3)/2=2нКл=2*10⁻⁹Кл,
Q₁=1*10⁻⁹Кл,  Q₂= 3*10⁻⁹ Кл,  R₂=2R₁ , F₁/F₂ -?
По закону Кулона F=k* q₁*q₂/R²,
F₁/F₂ = Q₁*Q₂ *R₂²/q₁*q₂*R₁² =3*10⁻¹⁸*(2R₁)²/4*10⁻¹⁸ *R₁² =3*4/4=3
Ответ: уменьшится в 3 раза

Answer 2

Calculation of the Initial Force of Interaction

To calculate the initial force of interaction between the two metal spheres with charges of 1 nC and 3 nC, we can use Coulomb's Law. Coulomb's Law states that the force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

The formula for Coulomb's Law is:

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

Where: - F is the force of interaction between the charges, - k is the electrostatic constant (approximately 9 × 10^9 Nm^2/C^2), - q1 and q2 are the charges of the two objects, and - r is the distance between the charges.

In this case, we have two spheres with charges of 1 nC and 3 nC. Let's assume the initial distance between them is 'd'.

Using Coulomb's Law, the initial force of interaction between the two spheres can be calculated as:

F_initial = k * (q1 * q2) / d^2

Now, let's move on to the next step of the problem.

Separating the Spheres and Calculating the New Force of Interaction

After bringing the two spheres into contact and then separating them to a distance that is twice the initial distance, we need to calculate the new force of interaction between them.

Let's assume the new distance between the spheres is '2d'.

Using Coulomb's Law, the new force of interaction between the two spheres can be calculated as:

F_new = k * (q1 * q2) / (2d)^2

To find the ratio of the new force to the initial force, we can divide the new force by the initial force:

F_new / F_initial = (k * (q1 * q2) / (2d)^2) / (k * (q1 * q2) / d^2)

Simplifying the equation:

F_new / F_initial = (2d)^2 / d^2

F_new / F_initial = 4

Therefore, the new force of interaction between the spheres will be 4 times smaller than the initial force of interaction.

Please note that the calculations provided above are based on the information given in the question and the application of Coulomb's Law.