The relationship of one of Maxwell's equations to Coulomb's Law

[MaestroBach]

My textbook tells me that one of Maxwell's equations, namely divergence of E = 4pi * charge density (in cgs) or divergence of E = pi / epsilon nought (in SI) is exactly equivalent to Coulomb's Law.

How in the world is that so?

Any ideas would be appreciated.

 

[Ibix]

Have you tried Googling? The Wikipedia page has a derivation - what don't you understand about it?

 

[Nugatory]

Any ideas would be appreciated.

Maxwell’s $\nabla\cdot\vec{E}=\rho/\epsilon_0$ can be rewritten in an integral form. Try applying that integral form to a spherical volume with a point charge in the center, and taking advantage of the symmetry of that configuration.

 

[Mister T]

Summary:: Maxwell vs Coulomb

My textbook tells me that one of Maxwell's equations, namely divergence of E = 4pi * charge density (in cgs) or divergence of E = pi / epsilon nought (in SI) is exactly equivalent to Coulomb's Law.

How in the world is that so?

The textbook doesn't explain?! Starting with either one, you can derive the other. Thus they are equivalent.