The electromagnetic force between two protons is much stronger than the gravitational force between them. Let Fe be the electromagnetic force, and Fg be the gravitational force. According to the problem: Fe=10nFg We write the formulas for both forces: Electromagnetic force: Fe=‌
1
4πε0
‌
e2
r2
Gravitational force: Fg=‌
Gm2
r2
Replace Fe and Fg in the equation: ‌
1
4πε0
‌
e2
r2
=10n‌
Gm2
r2
Since r2 is on both sides, it cancels out: ‌
1
4πε0
e2=10nGm2 Solve for 10n : 10n=‌
1
4πε0
‌
e2
Gm2
Now, use the constants: ‌
1
4πε0
=9×109 Charge of proton, e=1.6×10−19 Gravitational constant, G=6.67×10−11 Mass of proton, m=1.67×10−27 Plug in the values: 10n=‌
9×109×(1.6×10−19)2
6.67×10−11×(1.67×10−27)2
Calculate the numerator: 9×109×(1.6×10−19)2=9×109×2.56×10−38=2.304×10−28 Calculate the denominator: 6.67×10−11×(1.67×10−27)2=6.67×10−11×2.79×10−54=1.86×10−64 Divide the values: ‌