Question

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)=ke|q1q2|r2,F(r)=ke|q1q2|r2, where keke is Coulomb's constant, qiqi are the magnitudes of the charges of the two particles, and rr is the distance between the two particles.

(a)

To simplify the calculation of a model with many interacting particles, after some threshold value r=R,r=R, we approximate ff as zero.

Explain the physical reasoning behind this assumption.

What is the force equation?

Evaluate the force FF using both Coulomb's law and our approximation, assuming two protons with a charge magnitude of 1.6022×10−19coulombs (C),1.6022×10−19coulombs (C), and the Coulomb constant ke=8.988×109Nm2/C2ke=8.988×109Nm2/C2 are 11 m apart. Also, assume R<1m.R<1m. How much inaccuracy does our approximation generate? Is our approximation reasonable?

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

Answer 1

According to the scalar form of Coulomb's law: the force acting between the 2 charged particles in inversely proportional to the square of the distance between them.So, as the distance increases the Electrostatic force decreases fast and at some Threshold value its magnitude is small enough that it can be neglected relative to the other forces acting on the charged particle due to interactions with other particles.

The Force equation is given by:  

Force between 2 protons , 11 m apart given by Coulomb's law is:

As r=11m > R, using the approximation F(r)=0

The inaccuracy generated by the approximation is of which is very small in magnitude.

The approximation is thus reasonable.