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).
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.