# How to deduce Gauss' law from Gauss Divergence Law

## Homework Statement

Gauss Divergence Law:

Gauss' law

Can we obtain the Gauss' Law from Gauss Divergence Law?

## Homework Equations

In Spherical coordinates,

electric field strength

(Q/4$\pi$εr^2,0,0)
Then ∇$\cdot$E=0+0+0=0

## The Attempt at a Solution

We can not obtain the Gauss' Law from the general mathematical law?

## Answers and Replies

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UltrafastPED
Gold Member
So the volume integral of div E [application of Gauss' theorem to Gauss' law) is proportional to Q, the total charge included.

But Q is the volume integral of the charge density ... so we have a volume integral on both sides.

Then the integrands must be equal, which gives div E = densit/eps_0.

1 person
vela
Staff Emeritus
Homework Helper

## Homework Statement

Gauss Divergence Law:

Gauss' law

Can we obtain the Gauss' Law from Gauss Divergence Law?

## Homework Equations

In Spherical coordinates,

electric field strength

(Q/4$\pi$εr^2,0,0)
Then ∇$\cdot$E=0+0+0=0

## The Attempt at a Solution

We can not obtain the Gauss' Law from the general mathematical law?
There's a singularity in ##\vec{E}## at r=0 you need to account for.