# The unit of Flux density.

The unit of Electric flux is N.(m^2)/C. But how is it , that the Flux density(which is nothing but flux per unit area) has a unit of C/(m^2).?

Also , I have a book in Electromagnetic Engineering which states that "'electric displacement' and 'electric flux' are the same thing and both are equal to "Q" i.e the charge. It also states that the unit of flux is Coulomb.' Is all of this true?

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Born2bwire
Gold Member
The electric displacement field and the electric flux density are both the same thing, the vector D, which has units of C/m^2 in MKS. This differs from the electric field by the permittivity, the ratio of D/E is the permittiviy with units of F/m. The electric flux is related to charge using Gauss' Law, which states that the flux over a closed surface is equal to the total charge divided by the permittivity. So the electric flux is equal to (V/m)*(m^2) = V*m which is the same as N*m^2/C. Since the electric field and electric flux density are related by the permittivity, we can rewrite Gauss' Law to show that the integral of the electric flux density over a closed surface is equal to the total charge enclosed.

Yes. That's true.
But as I mentioned before, some books on Electromagnetic Engineering (like Jordan and Balmain), equate Electric flux to the amount of charge(i.e psi=Q). They have used the Faraday thought experiment of two concentric spheres for proving this equality.

I have never heard of this experiment before and I always know that the electric flux was nothing but the dot product of field and surface area over the whole gaussian surface ...
I could not understand this equality between flux and charge!!!

Born2bwire
Gold Member
Yeah I have seen that too, but the only previous time I have seen it was in the CRC Handbook of all places. The validity of the statement would be what they defined the electric flux to be and what units they are using. In the CRC Handbook, they defined the electric flux to be the integral of the electric flux density, not the electric field, and so that relationship would still be correct. Sometimes, people will choose a system of units where the permittivity and/or permeability of free-space are unity, this is common in the CGS units. Under these units, the same relationship would apply when defining electric flux to be the integral involving the electric field.

Im sorry, but I couldn't understand what you meant by

Sometimes, people will choose a system of units where the permittivity and/or permeability of free-space are unity, this is common in the CGS units. Under these units, the same relationship would apply when defining electric flux to be the integral involving the electric field.

Have they considered permittivity to be unity in the CRC handbook?

So what would be the correct equation of the flux? Would it be the integral of the electric field or the flux density?

Both definitions are possible.
There are 2 kinds of electric flux.
The flux of the E field with the unit V*m=N*m^2/C
and the flux of the D field with the unit C
Btw. the same is true for magnetic fields.
There is the B field which is the magnetic equivalent of the D field
and the H field - the magnetic equivalent of the E field.
So there are also 2 possible ways to define magnetic flux. In practice however engineers always use the flux of the B field.
That can be confusing. Because for electric fields they usually use the flux of the E field which correlates with the H field and not the B field.
Because of this students may think that magnetic flux behaves fundamentally differently from electric flux but that is not true. They are perfectly symmetrical.

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Thanks a million! I was really confused ( being an engineer and a physics enthusiast can therefore lead to clashing definitions of flux!) ...
Why, may i then ask, are there two types of electrical fluxes? is there any relation between the two( i.e " E flux" and "D flux")?
And why do engineers prefer the flux due to the D field..And what is the physical interpretation of this kind of flux?(faraday's experiment of concentric spheres leads to the definition of the D flux , if I am not wrong, but what does it exactly mean in layman terms?)

I'm not sure why there are 2 types. I guess each type has it's advantages and disadvantages.
There are different ways to think about it. You could think in terms of field lines.
Imagine there is a certain number of field lines emerging from each proton and the same number of field lines are entering each electron. Then the field lines would represent the D field i.e. "D flux".
If you use field lines to represent the "E flux" you can run into trouble because then the number of field lines doesn't stay constant anymore if they pass through different materials. But it really depends on the situation which one is easier to work with.
Of course there is a relation between the two. Look here http://en.wikipedia.org/wiki/Permittivity

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Born2bwire
Gold Member
Im sorry, but I couldn't understand what you meant by

Have they considered permittivity to be unity in the CRC handbook?

So what would be the correct equation of the flux? Would it be the integral of the electric field or the flux density?

Take a look at CGS Lorentz-Heaviside units. You will notice that the units have been chosen such that the flux, calculated using the electric field, is equal to the enclosed charge. There are some slightly different ways of working with Maxwell's equations. Sometimes people like to formulate them so that the inherent physics stands out without much distraction. Like the Lorentz-Heaviside units, it is easier to work with flux equal to charge than flux being equal to charge times some weird number. I prefer MKS myself because then there is no conversion between SI units, which are usually used for measurement, and the results of the equations.

On Dr. Zoidberg's comments, I am an engineer myself and I have seen that many engineering books like to make Maxwell's equations symmetric. So they call the B field the magnetic flux density and the H field the magnetic field. I have seen on numerous occasions that the reverse is true for physics references. They normally call the B field the magnetic field. But the engineer's way makes the formulas more symmetric. Sometimes we even add a ficticious magnetic charge and current and make them fully symmetric. But it should be noted that this magnetic charge and current are purely a computational tool and are not thought to be truely physical.

So they call the B field the magnetic flux density and the H field the magnetic field. I have seen on numerous occasions that the reverse is true for physics references. They normally call the B field the magnetic field.

I'd just like to point out that, while it is true many people call B the magnetic field, I do not think any reputable source will ever call H the magnetic flux density. When physicists call H the magnetic field, then they tend to call B the magnetic induction.

I have seen several places in the literature where people are calling B the magnetic field and H the magnetizing field. I, personally, am fond of this (new?) trend. Indeed, it makes perfect sense if you think about the conventional way of magnetizing a ferromagnetic rod and hysteresis plots.

Born2bwire