The following problems consider the scalar form of Coulomb's law, which describes the electrostatic force between two point charges, such as electrons. It is given by the equation F(r)=k_e frac left|q_1 q_2 right|r², where k_e is Coulomb's constant, q_i are the magnitudes of the charges of the two particles, and r is the distance between the two particles. To simplify the calculation of a model with many interacting particles, after some threshold value r = R, we approximate F as zero. a. Explain the physical reasoning behind this assumption. b. What is the force equation? c. Evaluate the force F using both Coulomb's law and our approximation, assuming two protons with a charge magnitude of 1.6022 times 10⁻¹⁹ coulombs (C), and the Coulomb constant k_e=8.988 times 10⁹ mathrmNm² / mathrmC² are 1 m apart. Also, assume R<1 m. How much inaccuracy does our approximation generate? Is our approximation reasonable? d. Is there any finite value of R for which this system remains continuous at R?
