# The average distance between the protons in the beam of the new particle accelerator at CERN is approx. 10^-4 m.Calculate the force acting between two neighbouring protons. Compare the result to...

The average distance between the protons in the beam of the new particle accelerator at CERN is approx. 10^-4 m.

Calculate the force acting between two neighbouring protons. Compare the result to the gravitational force acting between the 2 protons (ratio).

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### 1 Answer

A proton is a particle that has a mass of 1.672*10^−27 kg and a charge of 1.602*10^−19 C.

The gravitational force of attraction between two particles with mass M1 and M2 can be taken as G*M1*M2/r^2 where G is constant equal to 6.674*10^-11 N m^2*kg^-2 and r is the distance between the particles.

Similarly the electrostatic force of repulsion between two particles with charge C1 and C2 is given by C1*C2/4*pi*r^2*Eo, where r is the distance and Eo is a constant equal to 8.854*10^-12 F *m^−1

We can use the information we have of the mass and charge or the proton and the distance between them given as 10^-4 m to find the electrostatic force of repulsion as:

Ef = (1.602*10^−19*1.602)^2/4*pi*(10^-4)^2*8.854*10^-12

=> 2.3066*10^-32 N

The gravitational force of attraction is:

Eg = 6.674*10^-11*(1.672*10^−27)^2/ (10^-4)^2

=> 1.865*10^-56 N

**This gives the force of repulsion between the protons as almost 10^24 times the force of attraction between them.**