Electric Flux: Is it an Integer or a Real Value?

[aniketp]

I have a doubt about electric flux.
It is said to be the no. of field lines passing through a given area.
But then we integrate it as:
\int\vec{E}.\vec{ds}=\Phi
However, bein the number of field lines does it not have to be an integer?

 

[Ben Niehoff]

No, because "field lines" are not absolutely defined. They are merely streamlines of the E vector field, and their density represents the strength of the E field. So, you choose a particular "calibration" when you want to draw field lines; e.g., you might have 1 field line = 1 N/C, or you might have 1 field line = 1.5 N/C, etc., and you just draw the streamlines appropriately close together or far apart.

But if, say, your field strength at a particular point is 1.3 N/C, then this amounts to 1.3 "field lines" under some particular calibration -- a fractional number.

The electric field magnitude is proportional to the density of field lines at a particular point (i.e., field lines per area, taken as a limit as the area gets small). The electric flux is equal to the total field lines in a given area, which is simply integrating the density of lines over the area. It doesn't have to be an integer. For example, if your field lines in one particular place are a meter apart, and the area you're considering is a 45-90-45 triangle with base legs of 1 meter each, then the flux is 0.5 "field lines".

By the way, your formulas will be much more readable if you put the entire formula within one set of [ tex ][ /tex ] tags, rather than wrapping each character individually. For example, typing

[ tex ]\int \vec E \cdot \vec {ds} = \Phi[ /tex ]

will give you

\int \vec E \cdot \vec {ds} = \Phi

 

[aniketp]

so are field lines just a vague concept developed for better intuitive understanding?

 

[Ben Niehoff]

so are field lines just a vague concept developed for better intuitive understanding?

No, they're very real; I mean, the E field definitely has streamlines. It's just that they're a continuous number rather than an integer number--you can draw a field line at any point in space; not just at a certain set of discrete points.

 

[aniketp]

so it is just like where water has molecules but u can't count 'em.
I understood it now. Thanx.