Two protons in vacuum are held a distance apart

PHYSICS · Subjective · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Electrostatic fields and potential · Electrostatic fields and potential

Electricity, Magnetism and Electromagnetism, Ch Electric charge, Coulomb's law and the electric field

Problem

Two protons in vacuum are held a distance rr apart. Each has charge +e=1.602×10−19 C+e = 1.602\times10^{-19}\ \mathrm{C} and mass mp=1.673×10−27 kgm_p = 1.673\times10^{-27}\ \mathrm{kg}. Take k=1/4πε0=8.99×109 N m2 C−2k = 1/4\pi\varepsilon_0 = 8.99\times10^{9}\ \mathrm{N\,m^2\,C^{-2}} and the gravitational constant G=6.674×10−11 N m2 kg−2G = 6.674\times10^{-11}\ \mathrm{N\,m^2\,kg^{-2}}; the protons are treated as point particles and no other bodies are nearby. Show that the ratio of the Coulomb repulsion to the gravitational attraction between them does not depend on rr, and estimate its value. Give the ratio to two significant figures.

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