Gauss's law states that flux=charge/epsilon. Whereas all too often flux is equated to charge. I do not understand this paradox. Can anyone explain?
Tulika,
Gauss' theorem is properly that the electric flux through a closed surface is proportional to the total charge within that surface.
I have never heard of flux being *equated* to charge.
They have different dimensions for a start (and therefore different units).
Where do you find these quantities being equated?
Hello James,
Thanks for your reply!While deriving the capacitance of a parallel plate capacitor, the steps as mentioned in the attached doc are taken.Please have a look at athe attachment,In one of the steps flux is equated to the charge contained.
Tulika,
Thank you for the document.
I think that there is some confusion here between the displacement field, D, and the electric flux density.
The flux density is often shown as the greek letter phi, and has units in SI of V m.
The displacement field, D, is defined in a material as;
D = epsilon_0. E + P where P is the polaziation density.
This, after a little work, can be rewritten for a simple material as;
D = epsilon_0 (1 + chi).E
or
D = epsilon. E
where the field E is the applied field, and chi is the electrostatic susceptibility of the material (think of the analogous case in magnetism - how readily the material can be polarized)
So I agree that the displacement field is related to the free charges in the capacitor by;
D = Q/A (that's Gauss' law, but rewritten for a capacitor).
and
phi = Q / epsilon_0
but it is unphysical to then say D = phi. Phi has units of Vm (in SI), and D has units of C m^-2. One is a charge density, one is a field. Sure, they are related (Gauss), but may I suggest the derivation here?
D = Q/A (Gauss' theorem for a capacitor)
and
D = epsilon. E (definition of D)
So, Q/A = epsilon.E
but
E = V/d
thus
Q/A = V/d . epsilon
Q = A . V/d . epsilon
as
C = Q/V (by definition)
then
C = epsilon . A/d
beware two quantities with the same letter!
There's an excellent set of pages on wikipedia (which I admit, I had to resort to - it has been 25 years since I wrestled with this sort of matter).
Another way of looking at it is from the point form of the law; that DIV(D) = rho. In Physical terms, it states that lines of electric flux begin and end on an electric charge. So, if the the quantity of positive charges is the same as quantity of negative charges within a closed surface, then NET flux from the region enclosed is zero. If however, there are more of one that the other, then NET flux from (or into) the region through the closed surface assumes a non-zero value. You can now see why flux through a closed surface may be equated net charge enclosed by the surface . . .
Hi,
Thereis no paradox. The statment, "Gauss's law states that flux=charge/epsilon", is incorrect. Here, you must have considered flux=the integral of E (electric field) over a surface. In fact, flux=the integral of D (flux density) over a surface, while D=epsilon*E.
Hope this will help.
Jinxi
Tulika, look what is the difference between charge and flux(cluster of charge).,Implies in to gauss theroem and got the flux.
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