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

Click For Summary

Discussion Overview

The discussion revolves around the nature of electric flux and whether it should be considered an integer value, given its definition as the number of electric field lines passing through a given area. Participants explore the conceptual and mathematical implications of this idea.

Discussion Character

  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions if electric flux, defined as the number of field lines through an area, must be an integer.
  • Another participant argues that field lines are not strictly defined and can represent fractional values depending on the calibration of the field strength, suggesting that electric flux does not have to be an integer.
  • A participant explains that the density of field lines correlates with the electric field strength, leading to the conclusion that electric flux can be a continuous value.
  • There is a discussion about whether field lines are merely a conceptual tool for understanding electric fields, with some asserting they are real but continuous rather than discrete.

Areas of Agreement / Disagreement

Participants express differing views on whether electric flux should be considered an integer or a real value, indicating that the discussion remains unresolved with multiple competing perspectives.

Contextual Notes

The discussion highlights the ambiguity in defining field lines and electric flux, noting that the interpretation may depend on the chosen calibration and the continuous nature of the electric field.

aniketp
Messages
84
Reaction score
0
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:
[tex]\int[/tex][tex]\vec{E}[/tex].[tex]\vec{ds}[/tex]=[tex]\Phi[/tex]
However, bein the number of field lines does it not have to be an integer?
 
Physics news on Phys.org
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

[tex]\int \vec E \cdot \vec {ds} = \Phi[/tex]
 
Last edited:
so are field lines just a vague concept developed for better intuitive understanding?
 
aniketp said:
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.
 
so it is just like where water has molecules but u can't count 'em.
I understood it now. Thanx.
 

Similar threads

  • · Replies 9 ·
Replies
9
Views
2K
  • · Replies 25 ·
Replies
25
Views
3K
  • · Replies 11 ·
Replies
11
Views
2K
  • · Replies 24 ·
Replies
24
Views
2K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 30 ·
2
Replies
30
Views
3K
Replies
5
Views
2K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 5 ·
Replies
5
Views
1K
  • · Replies 35 ·
2
Replies
35
Views
5K