# Limit at which Strong Nuclear force = Electromagnetism

1. Oct 4, 2009

### 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.

2. Oct 6, 2009

### 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