Limitation of Coulomb's Law - QS Study
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Limitation of Coulomb’s Law

Coulomb’s law is extended method of the quantity 4π in MKS unit. This method is proposed by Oliver Heaviside and Lorentz in 1995.

Apparently, it appears that inclusion of the quantity 4π in Coulomb’s law creates some complication, although that quantity can be included deliberately into the equation. In other extensively used equation where the presence of the quantity 4π in absence of spherical symmetry and presence of the quantity 2π in absence of cylindrical symmetry, creates complication. In order to simplify those equations, an appropriate method of the unit is needed. For example in CGS unit, the capacitance is, C = A / 4πD e.s.u.

But in MKS or SI unit C =4πε0A / 4πd = (ε0A / d) Farad

From the idea of induction, it is seen that, the number at tubes of force passing through the area located perpendicular to the direction of electric field = ε E, where E = Electric field, ε = permittivity of the medium. The total induction in a plane can be calculated by Gauss’s law in that plane but total induction cannot be calculated by Coulomb’s law. Again, other than point charge magnitude of applied force in any other charged bodies cannot be determined by Coulomb’s law.

In short,

  • Coulomb’s law is valid if the average number of solvent molecules between the two interesting charge particles should be large.
  • Coulomb’s law is valid if the point charges are at rest.
  • It is difficult to apply the Coulomb’s law when the charges are in arbitrary shape. Hence, we cannot determine the value of distance ‘d’ between the charges when they are in arbitrary shape.