Question

Два одинаковых шарика, заряженные одноименными зарядами и помещенные на расстоянии 10 см друг от друга, отталкиваются с силой 0,12 мН. Их приводят в соприкосновение и затем снова разводят в прежнее положение. Шарики теперь отталкиваются с силой 0,16 мН. Найти заряды шариков до их соприкосновения. ПОДРОБНОЕ РЕШЕНИЕ ЗАДАЧИ!

Answer 1

Problem Analysis

We have two identical charged spheres that are initially placed 10 cm apart and repel each other with a force of 0.12 mN. After bringing them into contact and then separating them back to their original positions, the spheres now repel each other with a force of 0.16 mN. We need to find the charges on the spheres before they were brought into contact.

Solution

Let's assume the charges on the spheres are q1 and q2, and the distance between them is r.

According to Coulomb's Law, the force between two charged objects is given by:

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

where F is the force, k is the electrostatic constant, q1 and q2 are the charges, and r is the distance between the charges.

We are given the following information: - The initial force between the spheres is 0.12 mN. - The final force between the spheres is 0.16 mN. - The initial distance between the spheres is 10 cm.

Let's calculate the charges on the spheres using the given information.

Calculation

1. Convert the forces to SI units: - Initial force: 0.12 mN = 0.12 * 10^-3 N - Final force: 0.16 mN = 0.16 * 10^-3 N

2. Convert the distance to meters: - Initial distance: 10 cm = 10 * 10^-2 m

3. Substitute the values into Coulomb's Law for the initial force: - 0.12 * 10^-3 N = k * (|q1 * q2|) / (10 * 10^-2 m)^2

4. Substitute the values into Coulomb's Law for the final force: - 0.16 * 10^-3 N = k * (|q1 * q2|) / (10 * 10^-2 m)^2

5. Divide the equation for the final force by the equation for the initial force to eliminate the electrostatic constant: - (0.16 * 10^-3 N) / (0.12 * 10^-3 N) = (k * (|q1 * q2|) / (10 * 10^-2 m)^2) / (k * (|q1 * q2|) / (10 * 10^-2 m)^2)

6. Simplify the equation: - 0.16 / 0.12 = 1

7. Solve for the ratio of the charges: - |q1 * q2| / |q1 * q2| = 1

Since the charges on the spheres are identical, we can assume q1 = q2 = q.

8. Substitute q1 = q2 = q into the equation: - |q * q| / |q * q| = 1

9. Simplify the equation: - q^2 / q^2 = 1

10. Solve for q: - q = ±1

Therefore, the charges on the spheres before they were brought into contact are ±1.

Conclusion

The charges on the spheres before they were brought into contact are ±1.