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.

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Answers and Replies

Science Advisor
2022 Award
Have you tried Googling? The Wikipedia page has a derivation - what don't you understand about it?

Mentor
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.

Science Advisor
Gold Member
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.