Which constant is larger in magnitude: k (Coulomb's constant) or G (gravitational constant)?

Which constant is larger in magnitude: k (Coulomb's constant) or G (gravitational constant)?

• A. G (Gravitational Constant)
• B. k (Coulomb's Constant)
• C. They are equal in magnitude
• D. Cannot be compared

Answer: (B)

The main idea here is to compare how strong each fundamental force is as captured by its constant in the inverse-square laws. For electrostatic force, F = k q1 q2 / r^2, and for gravitational force, F = G m1 m2 / r^2. Since both forces fall off as 1/r^2, the relative strength comes from the constants (and the typical sizes of charges and masses). Coulomb's constant is about 8.99 × 10^9, while the gravitational constant is about 6.67 × 10^-11. That means k is larger by roughly 20 orders of magnitude. So, for comparable amounts of charge and mass, the electrostatic interaction is vastly stronger than gravity. This is why, on everyday scales, gravity is weak enough to be negligible compared with electromagnetism, yet it becomes the dominant force on astronomical scales when masses are large. Therefore, the larger-magnitude constant is Coulomb's constant.

The main idea here is to compare how strong each fundamental force is as captured by its constant in the inverse-square laws. For electrostatic force, F = k q1 q2 / r^2, and for gravitational force, F = G m1 m2 / r^2. Since both forces fall off as 1/r^2, the relative strength comes from the constants (and the typical sizes of charges and masses).

Coulomb's constant is about 8.99 × 10^9, while the gravitational constant is about 6.67 × 10^-11. That means k is larger by roughly 20 orders of magnitude. So, for comparable amounts of charge and mass, the electrostatic interaction is vastly stronger than gravity. This is why, on everyday scales, gravity is weak enough to be negligible compared with electromagnetism, yet it becomes the dominant force on astronomical scales when masses are large.

Therefore, the larger-magnitude constant is Coulomb's constant.