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.
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