Electrodynamics: divergence of E in empty space

[Flying_Dutchman]

What is the physical significance of fundamental law del.E=0 in free space ?

 

[Lord Jestocost]

Do you mean LaPlace's equation?
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/laplace.html

 

[Dale]

What is the physical significance of fundamental law del.E=0 in free space ?

It means there are no charges in free space.

 

[Flying_Dutchman]

Do you mean LaPlace's equation?
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/laplace.html

No I am talking about Maxwells equation in free space

 

[Flying_Dutchman]

It means there are no charges in free space.

del.E=P/e• which is one of the fundamental Maxwell's equation. We arrived at the conclusion that since there r no charges in free space because vacuum can't have any matter therefore del.E=0 . So isn't it wrong to conversely say that since del.E=0 there r no charges in free space when del.E=0 came from assuming that there can not be any Free charges in vaccum?

 

[Dale]

No, the converse is also true.
$\rho = 0 \implies \nabla \cdot \vec E =0$
and
$\nabla \cdot \vec E = 0 \implies \rho = 0$