# Electrical and gravitational forces of protons

• joel amos
In summary: So the answer is: At what distance between two protons are the electrical and gravitational forces equal?
joel amos

## Homework Statement

At what distance between two protons are the electrical and gravitational forces equal?

## Homework Equations

electromagnetic Force = k(Q1*Q2/r^2)
gravitational Force = G(m1*m2/r^2)

Constants:
k = 9.0*10^9 (N m^2/c^2)
G = 6.673 × 10^-11 (m^3 kg^-1 s^-2)
Charge of proton: 1.6*10^-19 C
Mass of proton: 1.67*10^-27 kg

## The Attempt at a Solution

I solved the first equation for r^2. Then, I substituted the second equation in for force since electromagnetic and gravitational force are equal in this problem. This seems logical, no? The only problem is, when I solve for r, the r's cancel out... :_(

Last edited:
At what value of $r$ does $kq^2 = Gm^2$?

joel amos said:

## Homework Statement

At what distance between two protons are the electrical and gravitational forces equal?

## Homework Equations

electromagnetic Force = k(Q1*Q2/r^2)
gravitational Force = G(m1*m2/r^2)

Constants:
k = 9.0*10^9 (N m^2/c^2)
G = 6.673 × 10^-11 (m^3 kg^-1 s^-2)
Charge of proton: 1.6*10^-19 C
Mass of proton: 1.67*10^-27 kg

## The Attempt at a Solution

I solved the first equation for r^2. Then, I substituted the second equation in for force since electromagnetic and gravitational force are equal in this problem. This seems logical, no? The only problem is, when I solve for r, the r's cancel out... :_(
When r approaches zero or when they are very close to one another, the gravitational force is as large as the electrical force. Both the forces approach infinity.
or
When r approaches infinity or when they are very far apart, the gravitational force and the electrical force approach zero.
Make sense? I'm not so sure.

But they don't approach zero or infinity at the same rate.

tms said:
At what value of $r$ does $kq^2 = Gm^2$?

I believe that the question is: At what value of $r$ does $(kq^2)/r^2 = Gm^2/(r^2)$?

Last edited:
joel amos said:
At what distance between two protons are the electrical and gravitational forces equal?
They're never equal.

joel amos said:
The only problem is, when I solve for r, the r's cancel out...
That's why.

LastOneStanding said:
They're never equal.
Okay, thanks!

joel amos said:
I believe that the question is: At what value of $r$ does $(kq^2)/r^2 = Gm^2/(r^2)$?
But, as you pointed out, the $r$s cancel.

## 1. What is the electrical force of a proton?

The electrical force of a proton is a fundamental force of nature that is responsible for the attraction and repulsion between charged particles. It is caused by the presence of electric charge on the protons, which can either be positive or negative.

## 2. How does the electrical force of a proton affect its behavior?

The electrical force of a proton plays a crucial role in determining its behavior. It is responsible for keeping the protons bound together in the atomic nucleus, as well as for the interactions between atoms and molecules. This force also determines the behavior of charged particles in electric and magnetic fields.

## 3. What is the gravitational force of a proton?

The gravitational force of a proton is a fundamental force of nature that is responsible for the attraction between all objects with mass. It is caused by the presence of mass on the protons and is directly proportional to the mass of the objects and inversely proportional to the square of the distance between them.

## 4. How does the gravitational force of a proton compare to its electrical force?

The gravitational force of a proton is significantly weaker than its electrical force. This is because the gravitational force is dependent on mass, which is much smaller than electric charge. The electrical force is also much stronger because it can be either attractive or repulsive, while the gravitational force is always attractive.

## 5. Can the electrical and gravitational forces of protons be measured?

Yes, the electrical and gravitational forces of protons can be measured using various instruments and techniques. For example, the electrical force can be measured using an electroscope, while the gravitational force can be measured using a balance scale or a gravimeter. These forces are also studied and measured in particle accelerators and other experimental setups in the field of physics.

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