Chapter 22, Problem 50EAP

Gravity vs. the Electromagnetic Force. The amount of electromagnetic force between two charged objects can be computed with an inverse square law similar to Newton’s universal law of gravitation; for the electromagnetic force, the law is $F=k\times \frac{\left(\text{Charge of object 1}\right)\times \left(\text{Charge of object 2}\right)}{d^2}$
In this formula, the charges must be given in units of coulombs (abbreviated C), the distance d between the objects’ centers must be in meters, and the constant  $k=9\times {10}^9\text{kg}\times {\text{m}}^3/\left(C^2\times s^2\right)$ .

1. Compute the gravitational force between your body and Earth using Newton’s universal law of gravitation (see Section 4.4 or Appendix B).
2. Now suppose all the electrons suddenly disappeared from Earth, making it positively charged, and all the protons in your body suddenly changed into neutrons, making you negatively charged. Compute the strength of the electromagnetic force between the electrons in your body and the protons in Earth. Assume that the charge per unit of mass of both you and Earth is  $5\times {10}^{7}C/\text{kg}$ .
3. Compare the electromagnetic force from part b to the gravitational force from part a. Use that result to explain why gravity is considered weaker than the electromagnetic force.