What is the significance of the fact that the gravitational constant, G, is a very small number and that Coulomb’s constant, k, is a very large number?

Question

The comparison indicates that the electromagnetic force is a much weaker force than the gravitational force.
The comparison indicates that the gravitational force is a much weaker force than the electromagnetic force.
The comparison does not give enough information to determine which force is weaker because the forces are in different units.

Answer 1

The correct interpretation of the significance of the gravitational constant $G$ being a very small number and Coulomb’s constant $k$ being a very large number is:

The comparison indicates that the gravitational force is a much weaker force than the electromagnetic force.

Here's the reasoning behind this conclusion:

• $G$ has a value of approximately $6.674\times {10}^{-11},{\text{N m}}^2/{\text{kg}}^2$, which is quite small.
• $k$ has a value of approximately $8.99\times {10}^9,{\text{N m}}^2/{\text{C}}^2$, indicating a much larger magnitude.

When considering both forces:

• The gravitational force is always attractive and acts between any two masses, but it is very weak compared to other fundamental forces.
• The electromagnetic force can be both attractive and repulsive and is much stronger than gravity, which is evident in the comparison of the constants.

In practical terms, for everyday scales, the gravitational force between two masses is negligible compared to the electromagnetic interactions experienced between charged particles.