# Electrical and gravitational forces of protons

1. Jan 30, 2013

### joel amos

1. The problem statement, all variables and given/known data
At what distance between two protons are the electrical and gravitational forces equal?

2. Relevant 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

3. 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: Jan 30, 2013
2. Jan 30, 2013

### tms

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

3. Jan 30, 2013

### Leong

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.

4. Jan 30, 2013

### tms

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

5. Jan 31, 2013

### joel amos

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

Last edited: Jan 31, 2013
6. Jan 31, 2013

### VantagePoint72

They're never equal.

That's why.

7. Jan 31, 2013

### joel amos

Okay, thanks!

8. Jan 31, 2013

### tms

But, as you pointed out, the $r$s cancel.