# Electrostatic Force Exerted Between Two Protons

• tjrana0
In summary, the question is asking for the distance at which a second proton should be placed near the surface of the Earth so that the electrostatic force it exerts on the first proton is equal to the weight of the first proton. Using the Coulomb equation and equating the weight to the electrostatic force, a distance of 0.118471m is calculated.

#### tjrana0

A proton is in a vacuum near the surface of Earth. Where should a second proton be placed so that the electrostatic force it exerts on the first proton balances the weight of the first proton?

F = (k×Abs[q1]×Abs[q2]) / r^2
k = 8.99×10^9 Nm^2/C^2

You need to post your attempt.

The first attempt, I got 1.51911E-14 which was incorrect.
It says "Did you use the Coulomb equation to get the electrostatic force? Do you recall how to calculate the gravitational force on an object (the weight) near Earth's surface?"
I did do all of the above, but with no success.

proton = 1.602176 10^-19;

Solve[1 == (k proton^2)/r^2, r]
{{r -> -1.51911*10^-14}, {r -> 1.51911*10^-14}}
This was the answer that was incorrect.
I thought that the left side of the equation was 1, for some reason, I'm not sure. If it is 0, then the equation is unsolvable. What did I do wrong?

tjrana0 said:
The first attempt, I got 1.51911E-14 which was incorrect.
It says "Did you use the Coulomb equation to get the electrostatic force? Do you recall how to calculate the gravitational force on an object (the weight) near Earth's surface?"
I did do all of the above, but with no success.

proton = 1.602176 10^-19;

Solve[1 == (k proton^2)/r^2, r]
{{r -> -1.51911*10^-14}, {r -> 1.51911*10^-14}}
This was the answer that was incorrect.
I thought that the left side of the equation was 1, for some reason, I'm not sure. If it is 0, then the equation is unsolvable. What did I do wrong?

If it is near the surface of the Earth, then a gravitational force acts on it, its weight, mg.

You want the weight to be the same the electric force.

So you need to equate mg to the formula for the electrostatic force.

I did 1.6762622*10^-27*9.80665 == 8.99*10^9*1.602*10^-19*1.602*10^-19/r^2
and solved for r and got the right answer! Thank you!

Solve[1.6762622*10^-27*9.80665 ==
8.99*10^9*1.602*10^-19*1.602*10^-19/r^2, r]
{{r -> -0.118471}, {r -> 0.118471}}

r=0.118471m

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## 1. What is electrostatic force?

Electrostatic force is the force exerted between two electrically charged particles. It is a fundamental force of nature that causes charged particles to either attract or repel each other.

## 2. How is electrostatic force calculated?

The electrostatic force between two charged particles is calculated using Coulomb's Law, which states that the force is directly proportional to the product of the two charges and inversely proportional to the square of the distance between them. The equation for Coulomb's Law is F = (k * q1 * q2) / r2, where F is the force, k is the Coulomb constant, q1 and q2 are the charges of the two particles, and r is the distance between them.

## 3. What is the electrostatic force exerted between two protons?

The electrostatic force exerted between two protons is the force of repulsion between them. As both protons have the same positive charge, they will repel each other with a force that follows Coulomb's Law. This force is very strong, but is counteracted by the strong nuclear force that holds protons together in an atom.

## 4. How does the distance between two protons affect the electrostatic force between them?

The electrostatic force between two protons is inversely proportional to the square of the distance between them. This means that as the distance between two protons increases, the force of repulsion between them decreases. So, the farther apart two protons are, the weaker the electrostatic force between them will be.

## 5. Can the electrostatic force between two protons be attractive?

No, the electrostatic force between two protons is always repulsive due to their positive charges. In order for the electrostatic force to be attractive, the charges of the particles must be opposite (e.g. a proton and an electron).