Two protons are aimed directly toward each other by a cyclotron accelerator with speeds of 2.30×105 m/s , measured relative to the earth. find the maximum electrical force that these protons will exert on each other

Explanation:

To keep the problem simpler, we can imagine that one proton is at rest and the second proton is approaching the first one with a speed which is twice the speed given, therefore:

According to the law of conservation of energy, the second proton will stop when all its kinetic energy has been converted into electric potential energy, therefore when

where

is the proton's charge

V is the electric potential at the final location of the proton

is the proton mass

The electric potential generated by the first proton is

where

is the Coulomb's constant

r is the minimum distance of approach of the second proton

Substituting all the quantities and solving for r, we find:

And so, the maximum electrical force between the two protons will be: