# Electrodynamics: divergence of E in empty space

• Flying_Dutchman
In summary, the physical significance of the fundamental law del.E=0 in free space is that it indicates the absence of charges in that space. This is derived from Maxwell's equation and is true in both directions - no charges implies del.E=0 and del.E=0 implies no charges.
Flying_Dutchman
What is the physical significance of fundamental law del.E=0 in free space ?

Flying_Dutchman said:
What is the physical significance of fundamental law del.E=0 in free space ?
It means there are no charges in free space.

Dale said:
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?

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

## 1. What is the concept of divergence in electrodynamics?

The concept of divergence in electrodynamics refers to the measurement of the flow of an electric field through a given point in space. It is a vector operation that helps in understanding how electric fields behave and interact with each other.

## 2. How is the divergence of the electric field calculated in empty space?

In empty space, the divergence of the electric field is calculated using the Gauss's Law, which states that the net electric flux through any closed surface is equal to the total charge enclosed by that surface. This can be represented mathematically as ∇ · E = ρ/ε0, where ∇ is the del operator, E is the electric field, ρ is the charge density, and ε0 is the permittivity of free space.

## 3. What does a positive or negative divergence of the electric field indicate?

A positive divergence of the electric field indicates that there is a net outward flow of electric field from a given point in space, while a negative divergence indicates a net inward flow. This can be visualized as electric field lines spreading out or converging towards a point, respectively.

## 4. How does the divergence of the electric field affect the behavior of charges in empty space?

The divergence of the electric field plays a crucial role in understanding the behavior of charges in empty space. A positive divergence indicates that charges are repelling each other, while a negative divergence indicates that charges are attracting each other. This can help in predicting the movement and distribution of charges in a given space.

## 5. Can the divergence of the electric field be non-zero in the absence of charges?

Yes, the divergence of the electric field can be non-zero in the absence of charges. This can happen when there is a changing magnetic field present, as described by the Maxwell-Faraday equation, which states that the curl of the electric field is equal to the negative rate of change of the magnetic field over time. This can result in a non-zero divergence of the electric field even in the absence of charges.

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