Chapter 2.4, Problem 168E

[T] The following problems consider the scalar form of Coulomb’s law, which describes the electrostatic force between two point charges, such as elections. It is given by the equation $F\left(r\right)=k_e\frac{\left|q_1{q}_2\right|}{r^2}$ where k_eis Coulomb's constant, $q_i$ are the magnitudes of the charges of the two particles, and r is the distance between the two particles. 168. To simplify the calculation of a model with many interacting particles, after some threshold value r = R, we approximate F as zero.

1. Explain the physical reasoning behind this assumption.

What is the force equation?

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 $k_e=8.988\times {10}^{9}N{m}^2/C^2$ are 1 m apart. Also, assume R < 1 m. How much inaccuracy does our approximation generate? Is our approximation reasonable?

Is there any finite value of R for which this system remains continuous at R?