You are given a sufficiently long piece of thread, a meter stick and a thin round shape iron rod. Explain how would you measure the diameter of iron rod by using given thread and meter stick.
This length = n x 2πr, where n is the no. of windings and r is the radius of the rod.
Therefore, the diameter of the rod = 2r = The length of wire used for ‘n’ windings /nπ
Why there is a 4π in Coulomb’s law?
Asked Rick Ghosh
This is a consequence of geometry.
Please remember that Coulomb’s law is stated originally for point charges at rest. By symmetry, a point charge should exert equal force on a test charge at all points equidistant from it, which constitute a spherical shell of surface area 4πr2.
This consideration itself suggests the inverse square relation ship as well as the need for 4π.
That was actually my explanation for it.
The term 4π was not there when Coulomb’s law was first stated in cgs system. The term 4π was introduced in SI on rationalization of units based on Maxwell’s equations of electromagnetism.
But I feel that my earlier explanation is simple and convincing.
Hope you got it.
Further discussions are welcome.