Question

Задача 1338 Одинаковые небольшые металлические шарики имеющие заряды -1,5 мКл и +2,5 мКл приходят в соприкосновение и вновь разносят на расстояние 6 см. Определить заряд каждого шарика и силу их взаимодействия

Answer 1

Q1 = -1,5 мКл
q2 = +2,5 мКл.
q = (q1+q2)/2 = (-1,5 + 2,5)/2 = 0,5 мКл = 5*10^(-4) Кл
F = k*q*q/(r^2),
k = 9*10^(9) Н*м/(Кл^2),
r = 6см = 0,06 м,
F = 9*10^(9) *5*10^(-4) * 5*10^(-4)/(6*10^(-2))^2 Н=
= 9*25*10/(36*10^(-4) ) Н = (9*25/36)*10^(5) Н = 6,25*10^(5) Н =
= 625 кН

Answer 2

Problem Analysis

We are given two small metallic spheres with charges of -1.5 mC and 2.5 mC. These spheres come into contact and are then separated by a distance of 6 cm. We need to determine the charge on each sphere and the force of their interaction.

Solution

When two charged objects come into contact, they can transfer charge between them until they reach equilibrium. In this case, the total charge before and after the contact remains the same.

Let's assume the initial charges on the spheres are q1 and q2, and the final charges after contact are q1' and q2'. According to the law of conservation of charge, we have:

q1 + q2 = q1' + q2' (Equation 1)

We are also given the charges on the spheres before contact:

q1 = -1.5 mC q2 = 2.5 mC

Substituting these values into Equation 1, we can solve for q1' and q2':

-1.5 mC + 2.5 mC = q1' + q2'

q1' + q2' = 1 mC (Equation 2)

Now, let's determine the charges on each sphere after contact.

To find the charges on the spheres after contact, we need to consider the ratio of their initial charges. Since the initial charge on sphere 1 is negative and the initial charge on sphere 2 is positive, the charge transfer will occur in such a way that the negative charge is reduced and the positive charge is increased.

Let's assume the ratio of charge transfer is x. Then we can write:

q1' = q1 - x q2' = q2 + x

Substituting these values into Equation 2, we get:

(q1 - x) + (q2 + x) = 1 mC

Simplifying the equation, we have:

q1 + q2 = 1 mC + 2x

Substituting the values of q1 and q2, we get:

-1.5 mC + 2.5 mC = 1 mC + 2x

1 mC = 1 mC + 2x

2x = 0

x = 0

This means that no charge is transferred between the spheres during contact. Therefore, the charges on the spheres after contact remain the same as their initial charges:

q1' = q1 = -1.5 mC q2' = q2 = 2.5 mC

Now, let's calculate the force of interaction between the spheres.

The force of interaction between two charged objects can be calculated using Coulomb's law:

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

Where: - F is the force of interaction - k is the electrostatic constant (k = 9 * 10^9 Nm^2/C^2) - q1 and q2 are the magnitudes of the charges on the spheres - r is the distance between the spheres

Substituting the values, we have:

F = (9 * 10^9 Nm^2/C^2) * (|q1| * |q2|) / r^2

F = (9 * 10^9 Nm^2/C^2) * (|-1.5 mC| * |2.5 mC|) / (0.06 m)^2

Calculating the values, we get:

F = (9 * 10^9 Nm^2/C^2) * (1.5 * 10^-3 C) * (2.5 * 10^-3 C) / (0.06 m)^2

F = 9 * 10^9 Nm^2/C^2 * 3.75 * 10^-6 C^2 / 0.0036 m^2

F = 9 * 3.75 * 10^3 N / 0.0036

F = 9 * 3.75 * 10^3 / 0.0036 N

F ≈ 9375000 N

Therefore, the force of interaction between the spheres is approximately 9375000 N.

Conclusion

The charge on each sphere remains the same after contact. The charge on the first sphere is -1.5 mC and the charge on the second sphere is 2.5 mC. The force of interaction between the spheres is approximately 9375000 N.