# Flux of electric field

Can anyone tell me the physical interpretation of the flux of an electric field through a closed surface. I think I do understand what flux is: Like in a water pipe a flux integral over the surface of the pipe would be the volume of water passing through the surface per second. What is the electric field dotted with the area? I've seen things like: It's the number of field lines passing through etc. but I don't like that picture, since field lines are not really a physical thing to me.

The flux is the electric field lines passing through the volume. The net flux is the sum of all field lines going in or out of a volume. For example, if you are at a great distance of a charged particle, the electrical field lines will be parallel. If you now draw a volume with 4 sides parallel to the flux direction, than the remaining two sides will cancel out (E1*n1dA1+E2n2dA1, where E1=E2, dA1=dA2 and n1=-n2), so there's no net flux in or out of that volume. When you move closer to the charge, however, the picture will change, but while the geometry changes the net flux will still be zero until you move so close to the charge that the charge is actually enclosed within your volume. When this happens the field lines no longer cancel each other out. There will be field lines going to the outside at all 6 sides of your volume. The net flux going in or out a volume is proportional to the electric charge in the volume.

HI Friendz,
There a positive charge q placed 'a' distance far from the center of a disc of radius 'r', on its axial line. The flux of charge on the disc is 1/4th of the total flux of the charge in the space. then deduce a relation between 'r' and 'a'.
the answer is "r = a / √3"

Philip Wood
Gold Member
z. As you say, if v is the velocity of fluid flow, v.dA is the volume of fluid passing through dA per second, i.e. the flux of fluid. So the definition of electric flux as E.dA is exactly analogous. For my taste, that's as far as I want to take the analogy; even this has the pedagogic drawback that it might suggest that something is moving through the area in the case of the electric field. I certainly don't find 'number of field lines passing through an area' very helpful.

I'm not sure you're going to find any deeper interpretation of the definition of electric flux. The definition proves its worth as soon as you state Gauss's Law.

Philip Wood
Gold Member
Th. A couple of hints...

(1) The flux from q that passes through the disc will pass through the spherical cap shown
in my diagram – hope I've got the set-up right.

(2) I've given you a formula (which you'll need) for the area of a spherical cap. You should try and prove it by integration.

With this information and a bit of algebra and elementary trig, you should be able to solve the problem. Incidentally, my answer wasn't quite the same as the one you gave. Quite possibly a slip on my part.

This isn't the only way to do the problem. You can integrate directly the flux passing through the disc, dividing the ring into annuli. You mustn't forget that the field strength changes from annulus to annulus, and so does the angle between the disc surface and the field.

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Edward M. Purcell's book "Berkeley Physics Vol2: Electricity & Magnetism" has me confused on the concept of electric flux.

On page 22 he has a diagram of flowing water implying (like zezima1 says above) that electric flux is analogous to the volume of fluid passing through a surface per unit of time--such as m^3/s

However, on page 24 he talks about bullets. He writes that field strength E is analogous to intensity of particle flow in bullets per unit area per unit time--bullets/m^2/s. He goes on to say that the flux of bullets through any surface surrounding the gun "is just the total number emitted per unit time" (bullets/second).

This is VERY confusing to me as I'm more familiar with neutron physics where the definitions are the OPPOSITE of what Purcell is describing. For instance a neutron source strength (Q) is measured in neutrons/second while neutron flux (phi) is rated in neutrons/cm^2/s.

I would appreciate some help in finding a way forward as this is a huge impasse.

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I'm not that familiar with nuclear physics, but I'd like to try to explain it with electrostatics.

The need to define an electric field has come from the observation that charges experience forces from other charges, they attract or repulse. The electric field is also defined as the force per unit charge. That's also all it is. The electric field is just a description of what forces charges would experience on various locations. The electric field is more of an abstract thing and not really a concrete physical thing. When we define the electric field as the force per unit charge it also means that there's nothing really moving around. Rather it's a description of how something (a charge) might move around when placed in the field. I think this is different from your nuclear flux and nuclear source strength.

In electrostatics we often talk of field lines which we use to represent the electric field. Electric field lines are as abstract as the electric field, but they are of great use in visualizing what happens. Now the field strength can indeed be described as something like bullets. It is important to note that it is a property of an area whereas the flux is a property of volume. Field strength describes how many field lines go through a certain area while electric flux describes how many field lines go in/out a volume.