Question

Пожалуйста, помогите! Два одинаковых маленьких металлических шарика с зарядами +q и -3q привели в соприкосновение и затем раздвинули на прежнее расстояние, гораздо большее, чем диаметры шариков. Силы взаимодействия между шариками ... ? (отношение) ВНИМАНИЕ! Решение есть, но оно не до конца понятно, поэтому, пожалуйста, больше подробностей.

Answer 1

До соприкосновения: F1=k**3q^2/R^2
После соприкосновения заhяды шариков стали одинаковыми, и равными Q-=(q1+q2)/2=(q-3*q)/2=-q
F2=k*q^2/R
F1/F2=3/1 

Answer 2

Interaction Forces between Charged Spheres

When two charged spheres come into contact and then are separated, they experience interaction forces due to their electric charges. In this case, we have two small metallic spheres with charges q and -3q, respectively. After they come into contact and are separated, the question asks about the ratio of the interaction forces between the spheres.

To understand the interaction forces between charged spheres, we can consider Coulomb's law, which states that the force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. Mathematically, Coulomb's law can be expressed as:

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

Where: - F is the magnitude of the force between the charges q1 and q2, - k is the electrostatic constant (k = 9 x 10^9 N m^2/C^2), - |q1 * q2| is the product of the magnitudes of the charges q1 and q2, - r is the distance between the charges.

In this case, we have two spheres with charges q and -3q. When they come into contact and are separated, the distance between them becomes much larger than their diameters. Let's denote the initial distance between the spheres as d.

Calculation of the Interaction Forces

To calculate the ratio of the interaction forces between the spheres, we need to consider the charges and the distances involved. Let's denote the force between the spheres after they are separated as F1, and the force between the spheres when they are in contact as F2.

When the spheres are in contact, they experience a force due to the attraction between the positive and negative charges. Since one sphere has a charge of q and the other has a charge of -3q, the magnitude of the force when they are in contact can be calculated using Coulomb's law:

F2 = k * (|q * (-3q)|) / (2r)^2

After the spheres are separated, the distance between them becomes much larger than their diameters. Let's denote the new distance between the spheres as D. The magnitude of the force between the spheres when they are separated can be calculated using Coulomb's law:

F1 = k * (|q * (-3q)|) / (2D)^2

To find the ratio of the interaction forces, we can divide F1 by F2:

Ratio = F1 / F2 = (k * (|q * (-3q)|) / (2D)^2) / (k * (|q * (-3q)|) / (2r)^2)

Simplifying the expression, we can cancel out the common terms:

Ratio = (2r / 2D)^2 = (r / D)^2

Therefore, the ratio of the interaction forces between the spheres is equal to the square of the ratio of the initial distance (r) to the new distance (D) between the spheres.

Please note that this explanation assumes point charges and neglects any other factors that may affect the interaction forces, such as the distribution of charges on the spheres or the presence of other charges in the surroundings.

I hope this explanation helps! Let me know if you have any further questions.