Final answer:
Coulomb's law is limited in that it requires stationary charges and does not apply at high speeds, large sizes, or strong external fields. The use of small wavelength probes disturbs the system, and Heisenberg's uncertainty principle limits the precision of measurements of physical properties.
Step-by-step explanation:
Coulomb's law describes the force between two point charges; however, it has several limitations. For the law to be applied accurately, the charges involved must be stationary, or if moving, they must be moving much slower than the speed of light – typically less than about 1% of the speed of light. Also, it assumes that the objects are of a sufficient size to be considered point particles, meaning they must be observable at least with a microscope, and that the charges are in a vacuum or uniform medium. Moreover, the charges should not be affected by significant external electric or magnetic fields, and only weak gravitational fields, such as the Earth's gravitational field, should be present.
Furthermore, the precision of observing and measuring the effects described by Coulomb's law is limited by the wavelength of the probe. Using very short wavelengths, like those in an electron microscope, can disturb the system being observed. Heisenberg's uncertainty principle also places a fundamental limit on the precision with which certain pairs of physical properties, such as position and momentum, can be known simultaneously. These constraints illustrate the limits of classical physics and point toward the need for quantum mechanics in explaining the behavior of extremely small particles.