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Closest approach of protons.


The problem is stated as follows:

Two protons are aimed directly toward each other by a cyclotron accelerator with speeds of 1500 km/s, measured relative to the earth. Find the maximum electrical force that these protons will exert on each other. Use 8.85*10^-12 F/m for the permitivity of free space, 1.60 *10^-19 C for the charge on an electron, and 1.67*10^-27 kg for the mass of the proton.

I have tried using the conservation of energy, where initial Kinetic Energy is equal to 1/2mv^2 and set this equal to the Potential Energy that exists when the protons are stopped due to repulsive forces. I then try to solve for r. Then I think this could be plugged back into find the potential V

V = kq/r

and with this information be able to find U and consequently E. I am not sure if I'm working in the right direction. Any advice is appreciated.

The Potential Energy I am defining as:

PE = q*V = q*E*r where r is the distance between the protons when E is at its max. then I think that :
E = U/q*d should yield the max electric field where d

Thank you.

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