The electric force is stronger than gravitational force by what factor?

The electric force is stronger than gravitational force by what factor?

• A. 10^20
• B. 10^30
• C. 10^10
• D. 10^40

Answer: (D)

Electric force dwarfs gravity by a huge amount. To compare them for the same separation, use F_e = k q1 q2 / r^2 and F_g = G m1 m2 / r^2. The ratio is F_e / F_g = (k q1 q2) / (G m1 m2). If you take typical elementary particles, the numbers give a very large factor. For two electrons, with q = e and m = m_e, the ratio works out to about 10^42. For two protons, it comes out around 10^36. Even with rough numbers, you’re looking at a factor on the order of 10^40. The main point is that the electromagnetic interaction is vastly stronger than gravity—by many tens of powers of ten—so the factor is around 10^40 in common estimates.

Electric force dwarfs gravity by a huge amount. To compare them for the same separation, use F_e = k q1 q2 / r^2 and F_g = G m1 m2 / r^2. The ratio is F_e / F_g = (k q1 q2) / (G m1 m2). If you take typical elementary particles, the numbers give a very large factor. For two electrons, with q = e and m = m_e, the ratio works out to about 10^42. For two protons, it comes out around 10^36. Even with rough numbers, you’re looking at a factor on the order of 10^40. The main point is that the electromagnetic interaction is vastly stronger than gravity—by many tens of powers of ten—so the factor is around 10^40 in common estimates.