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Why there is a 4(pi) in Coulomb’s law?

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Why there is a 4π in Coulomb’s law?

Asked Rick Ghosh

Answer:

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.

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