Question

Во сколько раз изменится сила взаимодействия между двумя точечными заряженными телами,если заряд одного из них увеличить в 3 раза; уменьшить в 3 раза? Срочноооо( чтобы было не только решение но и дано,СИ)

Answer 1

1)
q₁=3q₁        сила взаимодействия между 2-мя зарядами:
_______      F=kq₁q₂/R; заряд 1-го увеличили в 3 раза, тогда сила стала:
F₁-?              F₁=k3q₁q₂/R₂=3F;
                    Ответ: сила F₁ увеличилась в 3 раза.
2) 
q₁=q₁/3              F=kq₁q₂/R²;
_______            F₁=k(q₁q₂/3)/R²=F/3;
F₁-?                 Ответ: сила  F₁ уменьшилась в 3 раза.

Answer 2

Calculation of the Change in the Force of Interaction

To calculate the change in the force of interaction between two point charges when the charge of one of them is increased or decreased, we can use Coulomb's Law. Coulomb's Law states that the force of interaction between two point charges 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 (k = 8.99 x 10^9 N m^2/C^2) - q1 and q2 are the charges of the two point charges - r is the distance between the charges

Let's consider two point charges, q1 and q2, and calculate the change in the force of interaction when the charge of one of them is increased or decreased.

1. When the charge of one of the point charges is increased by a factor of 3: - Let's assume the initial charges are q1 and q2. - After increasing the charge of one of the point charges by a factor of 3, the new charges become 3q1 and q2. - The force of interaction between the charges can be calculated using Coulomb's Law with the new charges. - The new force of interaction, F', can be calculated as: F' = k * (3q1 * q2) / r^2

2. When the charge of one of the point charges is decreased by a factor of 3: - Let's assume the initial charges are q1 and q2. - After decreasing the charge of one of the point charges by a factor of 3, the new charges become q1/3 and q2. - The force of interaction between the charges can be calculated using Coulomb's Law with the new charges. - The new force of interaction, F'', can be calculated as: F'' = k * ((q1/3) * q2) / r^2

Now, let's calculate the change in the force of interaction for both cases.

Calculation of the Change in the Force of Interaction when the Charge is Increased

The change in the force of interaction, ΔF, when the charge of one of the point charges is increased by a factor of 3 can be calculated as:

ΔF = F' - F

Substituting the values into the equation:

ΔF = (k * (3q1 * q2) / r^2) - (k * (q1 * q2) / r^2)

Simplifying the equation:

ΔF = k * (3q1 * q2 - q1 * q2) / r^2

ΔF = k * (2q1 * q2) / r^2

Calculation of the Change in the Force of Interaction when the Charge is Decreased

The change in the force of interaction, ΔF', when the charge of one of the point charges is decreased by a factor of 3 can be calculated as:

ΔF' = F'' - F

Substituting the values into the equation:

ΔF' = (k * ((q1/3) * q2) / r^2) - (k * (q1 * q2) / r^2)

Simplifying the equation:

ΔF' = k * ((q1/3) * q2 - q1 * q2) / r^2

ΔF' = k * (-2q1 * q2/3) / r^2

Please note that the above calculations assume that the distance between the charges remains constant.