# Repulsion between two small spheres

• objective33
In summary, using the formula for electric force between two charged objects, we can calculate the force of electric repulsion between two small spheres placed 1.0 m apart, each with a deficit of 1.0 x 10^8 electrons. By plugging in the values for the charges and the distance between them, we can find the force to be 2.3 x 10^-12 N. The gravitational constant and the charge of one electron were used in the calculation.

## Homework Statement

Calculate the force of electric repulsion between two small spheres placed 1.0 m apart if each has a deficit of 1.0 x 10^8 electrons.

## Homework Equations

N = q/e
qe = mg
q = mg / e
q = mgr / Vb
e = 1.602 x 10^-19 C.
k = 9 x 10^9 - not sure if relevant or not.
Fe = qe
Answer ( as stated in the textbook): 2.3 x 10^-12N

## The Attempt at a Solution

Fe = qe?
r = 1. 0 m
e constant used
g = 9.8 N/kg?
Fe = (1.0 x 10^8 C)( 1.6 x 10^-19 C)x (1.0m/9.8N/kg) = 1.63 x 10^-12 N.

Last edited:
Through my reasoning, I found the answer.

Charge of one electron = 1.602 x 10^-19 C
Charge of a sphere = 1.602 x 10^-19 x 1.0 x 10^8 C

F = (1/4piÈ) Q1Q2/d^2
(1/4piÈ) is a constant equal to 9 x 10^9
F = 9x10^9 x (1.602x10^-11) x (1.602x10^-11) / 1
F = 2.3 x 10^-12 N

I would like to provide the following response to this content:

The force of electric repulsion between two small spheres can be calculated using the equation Fe = q1q2/r^2, where q1 and q2 are the charges on the spheres and r is the distance between them. In this case, the charge on each sphere can be calculated using the equation q = mg/e, where m is the mass of the sphere and e is the elementary charge. Assuming a mass of 1 gram for each sphere and using the given deficit of 1.0 x 10^8 electrons, we can calculate the charge on each sphere to be 1.0 x 10^-10 C. Plugging this into the equation for force of electric repulsion, along with a distance of 1.0 m, we get a value of 2.3 x 10^-12 N, which matches the answer given in the textbook. It is worth noting that the constant k, which represents the Coulomb constant, is not needed in this calculation since it is already accounted for in the units of charge and distance used. Additionally, the value of g, which represents the acceleration due to gravity, is not relevant in this calculation as it is not related to the force of electric repulsion between the spheres.

## 1. What causes repulsion between two small spheres?

The repulsion between two small spheres is caused by the electrostatic force between their electric charges. This force is a result of the interaction between the electrons in the outermost shells of the atoms that make up the spheres.

## 2. How does the distance between the spheres affect the repulsive force?

The repulsive force between two small spheres is inversely proportional to the square of the distance between them. This means that as the distance between the spheres increases, the repulsive force decreases.

## 3. What is the relationship between the size of the spheres and the repulsive force?

The repulsive force between two small spheres is directly proportional to the product of their charges and inversely proportional to the square of their radii. This means that as the size of the spheres increases, the repulsive force also increases.

## 4. Can the repulsive force between two small spheres be overcome?

Yes, the repulsive force between two small spheres can be overcome by a stronger attractive force, such as the force of gravity. This is why objects can come into contact with each other, despite having electric charges that would normally cause repulsion.

## 5. How is the repulsive force between two small spheres related to the concept of Coulomb's law?

The repulsive force between two small spheres is an example of Coulomb's law, which 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. In the case of two small spheres, this force is purely repulsive due to the like charges of the spheres.