Chapter 32, Problem 13A

The proportionality constant k in Coulomb’s law is huge in ordinary units, whereas the proportionality constant G in Newton’s law of gravity is tiny. What does this mean in terms of the relative strengths of these two forces?

To determine

To explain: The meaning of given statement in terms of relative strengths of electrical forces and gravitational forces.

Answer to Problem 13A

The electrical force is stronger than the force of gravity.

Explanation of Solution

Introduction:

According to inverse square law, a force applied on any two objects or charges is inversely proportional to the square of the distance between them and the directly to the product of masses.

The proportionality constant used in the electrical forces is “K”, whose value is $9\times {10}^9\text{ N}\cdot {\text{m}}^2{\text{/C}}^2$ . It is applied between two charged particles whose masses are too smaller. It is assumed that $1\text{ C}$ charge is the mass of a single electron. But, it is the masses of $6.24\times {10}^{18}$ electrons.

However, the proportionality constant used in the force of gravity is “G”, whose value is $6.67\times {10}^{-11}\text{ N}\cdot {\text{m}}^2{\text{/kg}}^2$ . It is applied between two masses of a kg each when they are a meter apart.

With the numerical value, it is clear that the proportionality constant applied in the electrical force is too much greater than the gravitational proportionality constant.

Conclusion:

Thus, it can be concluded that the electrical force is too much stronger as compared to the force of gravity.