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Mathematically, the potential of weak interactions is given by
V(r)=αW(e^−r/a)/r⇐ weak potential
V(r)=αEM1/r⇐ electromagnetic potential
For the weak potential, the parameter a controls the range of the force.
This type of potential is called a Yukawa potential.
Taking a=210^−18 m
and assuming αW=αEM,
what are the ratios of the weak potential to the EM potential at r=210^−20 meters? Give answer to two significant figures.

Hello Arkadeep,

This is really just a math problem. I'll give you a little help and you can do the rest.

Since we assume αW=αEM, the weak potential becomes
V(r)=αW(e^−r/a)/r = αEM * (e^−r/a)/r

So the ratio of the weak potential/electromagnetic potential is
(αEM * (e^−r/a)/r) / αEM1/r

Simplify that further and plug in 210^−20 meters for r.

I hope this helps,


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Steve Johnson


I would be delighted to help with questions up through the first year of college Physics. Particularly Electricity, Electronics and Newtonian Mechanics (motion, acceleration etc.). I decline questions on relativity and Atomic Physics. I also could discuss the Space Shuttle and space flight in general.


I have a BS in Physics and an MS in Electrical Engineering. I am retired now. My professional career was in Electrical Engineering with considerable time spent working with accelerometers, gyroscopes and flight dynamics (Physics related topics) while working on the Space Shuttle. I gave formal classroom lessons to technical co-workers periodically over a several year period.

BS Physics, North Dakota State University
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