Limit at which Strong Nuclear force = Electromagnetism

[daviddanut]

Is there a defined distance at which Electromagnetism starts exerting more force than the strong nuclear force?

So far I have

Gluons have <20MeV (32.04×10-13J) of energy.
Using the uncertainty principle:

t=h/(4×pi×E) and distance = t×c

Therefore t = (6.6×10^-34)/(4×pi×<32.04×10^-13) =<1.639×10^-23s
Therefore d = <1.639×10^-23 × 3.0×10^8 = <4.9×10^-15m

So the strong nuclear force has a maximum range of 4.9×10^-15m

The electromagnetic force has an infinite range, but it's force is proportional to the inverse square of the radius, so it drops exponentially.
F=(q1*q2)/(4×pi×ε0×r^2)

Where q1 + q2 are the charges of repelling particles, in this case 2 hydrogen nuclei and ε0 is the permittivity of a vacuum (as the space inside an atom is a vacuum)

The force at the limit of the Strong Nuclear force's range is:

F=(1.6×10^-19×1.6×10^-19)/(4×pi×8.85×10^-12×(4.9×10^-15)^2)) = 9.59 N

Is there anyway to link these two equations to get a definite limit? I'm attempting to explain the basics of fusing 2 hydrogen nuclei.

 

[Meir Achuz]

The gluon mass you used is an exptl upper limit. The gluon is expected to be massless like the photon. There are two types of "nuclear force" to consider. One is the force between quarks inside hadrons. The other is the effective force between baryons, which has a range of about 1 fm and is about 10 times stronger than the EM force. I think this is the force you should compare to the EM force. The equation you want is exp(-r/R)=e^2/g^2, where
R~1fm and e^2/g^2~0.1

 

[sir-pinski]

Unfortunately, there is no defined distance at which electromagnetism starts exerting more force than the strong nuclear force. The equations used to calculate the range and force of each force are based on different principles and cannot be directly linked. The strong nuclear force is responsible for binding particles within the nucleus, while electromagnetism is responsible for the interactions between charged particles.

Additionally, the strength of the strong nuclear force varies depending on the distance between particles, so there is no single limit that can be determined. It is also important to note that the strong nuclear force is the strongest force at very small distances, but at larger distances, the electromagnetic force becomes dominant.

Furthermore, the process of fusion requires not only overcoming the repulsive forces between two positively charged nuclei, but also overcoming the strong nuclear force that holds the nuclei together. This requires a lot of energy, which is why fusion reactions often occur in high energy environments such as stars.

In summary, while the calculations for the range and force of the strong nuclear force and electromagnetism can give us some understanding of their behaviors, there is no definite limit at which one force becomes stronger than the other. Both forces play crucial roles in the interactions between particles, and their strengths and ranges are dependent on various factors.