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## sristykrishnaprasad 4 years ago Is it possible to count the number of flux lines around a charged particle? Surely there can't be infinite since infinite line will mean infinite field strength. What could be that finite number?

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1. Owlfred

Hoot! You just asked your first question! Hang tight while I find people to answer it for you. You can thank people who give you good answers by clicking the 'Good Answer' button on the right!

2. ankurchiitd

Since the amount of flux in one flux line is not quantified it is always possible to have infinite number of lines. Much like it is possible to have infinite rectangles under the curve when you integrate to find its area. Comparing the density of field lines is a relative process and can be used to judge the relative strength of two fields - however it does not have much significance while talking about an isolated field. Hope this helps!

3. sristykrishnaprasad

Ankurch, is it possible to quantify the relative field strength if field due to one charge configuration is known and the 'relative' flux distribution due compared to the known charge configuration is mentioned for an unknown configuration?

4. ankurchiitd

I am not sure I get the question completely! Please elaborate. What I gather is that in the end you are curious as to whether field density ha s unit of sorts.. Am I on the right track?

5. sristykrishnaprasad

Say u have two charge configurations A and B. U are given the electric field strength due to A. Also, u are given a pictorial view of field lines due to A and B. Since u said it is a relative measure, is it now possible to quantify the electric field strength at a point due to B?

6. ankurchiitd

See the field lines are just a representation tool - so if the person who drew the lines drew them to be accurate when compared (the two field line configurations) then yes we can use this picture to determine field strength due to B.

7. sristykrishnaprasad

Can you elaborate ur view on 'accurate' drawing? In what can it be accurate?

8. ankurchiitd

It should be accurate in the fact that "the field line density should correspond to the field strength at the point".

9. gokuldas_tvm

I remember reading in several books that 'flux line' concept is not an accurate one. It often leads to confusing results. Don't depend on it to calculate any field strength

10. gokuldas_tvm

You can however calculate flux - but not in terms of lines

11. sristykrishnaprasad

Ankur, it means that for a given value of field strength a known density of lines should exist. This will take us back to our starting point that it is infact possible to count the number of flux lines in a region of space.

12. sristykrishnaprasad

gokul, yes flux is equal charge enclosed.

13. ankurchiitd

:-) No, it does not mean that for a given field strength a known density should exist. One, it is always comparative and two, it assumes that the depiction is "accurate".

14. gokuldas_tvm

sristy, you can draw any number of lines for a given field over an area - even infinite. The concept of flux lines should be used only for illustration. However, to show that a field is stronger over an area, you draw more lines through it. The only problem is that you can arbitrarily chose how many you want to draw

15. sristykrishnaprasad

I believe we are revolving around the same point again. If known density doesnt exist then it impossible to quantify field in the case of A and B systems i mentioned above. If u say only accurate depictions work then it shld be atleast possible to count the number of lines in such 'accurate' depictions.

16. ankurchiitd

@gokuldas_tvm: exactly!

17. ankurchiitd

@gokuldas_tvm: any analogy of a similar depiction tool usage?

18. gokuldas_tvm

@ankur: can't come up with any right now. But, i think - we need a strong description for 'flux'!

19. gokuldas_tvm

sristy: Concepts of 'flux' and 'flux lines' are slightly different. 'Flux density' refers to density of 'flux', not of 'flux lines'

20. ankurchiitd

@gokuldas_tvm: Physics grad? and I suppose the tvm stands for Thiruvananthpuram?

21. gokuldas_tvm

@ankur: TVM does stand for trivandrum! :D I am not a physics grad, but of electronics and communication. But Maxwell's equations and vector PDEs has always been one of my favourites.

22. ankurchiitd

@gokul: Cool.

23. gokuldas_tvm

@Ankur: Are you from around here?

24. ankurchiitd

@Gokul: Am from Delhi - an engineering physics grad.

25. gokuldas_tvm

@Sristy: I have a slightly more detailed idea on flux and fields. Interested?

26. sristykrishnaprasad

@gokuldas_tvm : surely sir

27. gokuldas_tvm

@Sristy: no need to call me sir. Anyway, imagine a 3D space, with each point denoted by x, y and z coods. Now imagine that there is a vector value at each of these points. ie, For any point you take, you get a vector. This is a 'vector field'. Examples include electric and magnetic fields.

28. sristykrishnaprasad

@gokuldas: So, in connection with my question how shall i appreciate ur logic?

29. gokuldas_tvm

This is important for understanding flux. The next point is about that

30. gokuldas_tvm

Now consider a surface within that 3D space. You can imagine that this surface will contain many points in the 3D space. And each of those points will have a vector associated with it. Now imagine accumulating all these vectors on the surface. ie, integrate the vectors on the surface. $\phi = \int\limits_{}^{}\int\limits_{}^{s} F.ds$ This value is a scalar which represents all total quantity of the vector crossing the surface. This will be a single number (a scalar). This is the flux.

31. sristykrishnaprasad

@gokul: apparently u are interested in Maxwell's equations. Hm?

32. gokuldas_tvm

yes

33. sristykrishnaprasad

Can u tell me whether Maxwell's equations are linear or non-linear?

34. gokuldas_tvm

I doubt that the equations themselves are linear or non-linear. Their solution could be perhaps classified as linear or non-linear

35. sristykrishnaprasad

Hmm point taken

36. gokuldas_tvm

I am not seriously sure about that - I have never done such an analysis on Maxwell's equation. I am only going through a book on non-linear systems now. Normally, you should be able to separate out linear and non-linear systems from partial differential equations like maxwell's equations. I am a little confused about this - because most results are linear. But I have also seen non-linear behaviour called 'solitons'. I am still to make any sense of that.

37. him1618

i think Q/epsilon naught represents the nmber of flux lines

38. gokuldas_tvm

@him1618: Q/E represents flux, not flux lines. Flux is the scalar product of the field and the surface, integrated over the entire surface. It is a scalar. The concept of flux lines is very misleading - because you can have them at every point on the surface. Thus you can have infinite flux lines. A lot of leading authors advice against using the 'flux line' concept, precisely because of this confusion. This includes the famed Dr. Richard Feynman.

39. him1618

@gokuldas: it represents the relative number of field lines coming out of a charged particle or going into it as well

40. gokuldas_tvm

@him1618: Hmm, Now I understand why Dr. Feynman so religiously opposed the flux line concept. Let us check how many flux lines are possible through a surface. There are 2 key facts: 1. In a vector field like electric field, every point in space is associated with a 3D vector (eg: the E vector). 2. A flux line is an imaginary curve (or line) that follow the direction of these vectors from a point to the next. Now consider a surface. It has infinite number of points on it. And each one of these points has a vector. You can associate each of these vectors with a flux line. Thus you have as many flux lines as you have points - ie, infinite number of flux lines! The danger in introducing the 'flux line' concept is that it leads people into thinking that the field (say electric field, or gravity field) exists as a bunch of strings. And then you would try to count them! Dr. Feynman used to oppose this concept - saying that only the 'field' concept is real. In other words, you have to consider the field as a hazy cloud of 3D vectors. You simply cannot separate it into lines and count it.

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