Why Do Different Sources Show Varying Electric Flux Equations?

[Jimmy84]

Homework Statement

Im starting to read about the electric flux and gauss's law. I am reading two books, Serway and Schaums electromagnetics.

The weird thing is that I'm getting different equations for the electric flux

Serway says that the Electric flux ψ is ∫E ds = 1/ε ∫ρ dv = Q/ε

While in other books I found that The Electric flux ψ is ∫ρ dv = Q

What is the real Electric flux equation ?

Thanks a lot.

Homework Equations

The Attempt at a Solution

 

[TSny]

In Schaum's, is the flux ψ defined in terms of the field E or the field D?

 

[Jimmy84]

In Schaum's, is the flux ψ defined in terms of the field E or the field D?

it is defined in terms of D

as ∫D ds = Q = ψ

 

[TSny]

Ok, that should account for the difference if you look at the relationship between E and D.

 

[Nickie]

The electric flux equation can be expressed in multiple ways, but they all represent the same concept. One of the most common forms is ∫E⋅dA = Q/ε₀, where E is the electric field, dA is the area element, Q is the enclosed charge, and ε₀ is the permittivity of free space. This equation is derived from Gauss's law, which states that the electric flux through a closed surface is equal to the enclosed charge divided by the permittivity of free space.

In terms of the equations you have mentioned, both are correct in different contexts. The first equation, ∫E ds = 1/ε ∫ρ dv = Q/ε, is used when calculating the electric flux through a closed surface with a known electric field and charge distribution. The second equation, ∫ρ dv = Q, is used when calculating the electric flux through an open surface with a known charge distribution.

It is important to note that the electric flux is a scalar quantity and can be expressed in different ways depending on the situation. Therefore, both equations are valid and represent the same concept. It is important to understand the context in which each equation is used and how they are derived from Gauss's law.