Question

A.) What is a power law? What does it mean for a quantity like the electric field to drop off as a power law?

B.) Does the electric field always drop off as r^-2, or can it drop off faster?

C.) Can the Coulomb force do work on a mass? What is required for this to happen?

Answer 1

A) The power law is a functional relationship between two quantities, such as intensity of a source and distance from it, where a relative change in one quantity(distance from the source) results in a proportional relative change in the other quantity(intensity of the source at that distance).

The electric field of a charge configuration changes as

where r is the distance from the charge configuration and k is a number. k can either be integer or non-integer depending on how the charge is distributed

B) According to Coulomb's law, the electric field for a point charge is

which means the electric field reduces as you go farther away from the charge according to the above equation

The above equation (field dropping off as is valid for point charge

It can drop even faster for a dipole. For a dipole the electric field at a distance r away from the dipole is

which means it drops as the 3rd power of r away from the dipole

C) The Coulomb force will not do work on a mass. It can do work provided the mass carries a certain amount of charge since the Coulomb force is the force working on only charged objects