# virtual wall between the magnetic fields generated by two wires...

#### PG1995

Joined Apr 15, 2011
816
Hi

Regards
PG

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#### t_n_k

Joined Mar 6, 2009
5,447
Hi

Regards
PG
The magnetic field in the region surrounding the wires is simply the result of the the current in each of the wires. The magnetic field strength [&/or flux] and direction at any point can be calculated for simple cases like this if the necessary physical parameters and associated assumptions are known.

If the 'wall' concept helps your understanding that's OK. I doubt it would satisfy a serious student of physics as an explanation.

#### PG1995

Joined Apr 15, 2011
816
Thank you, t_n_k.

So, you do agree that the 'yellow' and 'green' field won't get mingled into each other.

Best wishes
PG

#### t_n_k

Joined Mar 6, 2009
5,447
No - Sorry I don't agree because the explanation you offer has no meaning for me. It's as if an 'observer' [ignorant of the physical conditions producing the effect] located in the spatial field could somehow determine which wire current was producing what percentage of the effective flux or field strength at some point.

As I said if the the explanation helps you then by all means use it. I'd be wary in offering it as an explanation [say] in an examination.

#### PG1995

Joined Apr 15, 2011
816
Hi

Thank you.

Regards
PG

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#### steveb

Joined Jul 3, 2008
2,436
Thank you, t_n_k.

So, you do agree that the 'yellow' and 'green' field won't get mingled into each other.

Best wishes
PG
I understand t_n_k's point, that the net field is the sum of all sources; but I do agree that those fields lines will not cross. In this simple geometry it is not hard to visualize wires that are infinitely far away being brought together. Since field lines can not cross each other and since the directions are opposite, there really will be a non mixing of the field lines, from this point of view.

Faraday was the one who thought in terms of field lines rather than mathematical equations. Many criticized this but Maxwell embraced these concepts, and recognized field lines as valid mathematical constructs.

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#### steveb

Joined Jul 3, 2008
2,436
Hi

Thank you.

Regards
PG
For Q1, you are being asked to think in terms of superposition. The idea is that the net field can be equated to the sum of fields from individual pieces. When you think about the field of one piece, you have to mentally remove the other piece. You can't use the final solution, with the shown field lines, as a basis to say that the bottom part does not contribute fields to the upper part. So, even though the net field is zero (or small), the zero might be the result of a summation of nonzero things.

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#### steveb

Joined Jul 3, 2008
2,436
For Q2, it's not always easy to answer why a calculation gives a certain result. Sometimes you need to just get comfortable with the answer and then try to visualize it in various ways. In this example, the combined effect of an infinite number of loops, spread out over distance, has the effect of rendering the loop radius unimportant for determining the field at the center. Even though the loops far away should have less effect, there are an infinite number of them all contributing to the final solution. Predicting the result before doing the calculation might not be all that easy, but once you have the answer and spend some time thinking about superposition, it should begin to make intuitive sense.

Take another example of a charge distributed uniformly over an infinitely large flat plane. Above the plane, the electric field is everywhere constant, no matter how far away you are from the plane. At first this seems strange, but if you think of the infinite plane as the surface of an infinitely large sphere, then maybe it begins to make sense when you think about Coulomb's law.

Basically, you need to begin to develop techniques for visualization of field distributions. The ideas of superposition, field lines and known solutions to simple examples all help in this process. There is no one right way to cover all the bases, and each person might find some methods better than others.

By the way, the fact that you asked this question shows that you are thinking correctly. You are naturally trying to develop the correct thought processes and visualize the answers.

#### #12

Joined Nov 30, 2010
18,190
Since field lines can not cross each other and since the directions are opposite,
Please clarify. I see the rotation of the fields as opposite but I see the lines in between the conductors as going in the same direction as each other. My frame of reference needs adjusting.

#### steveb

Joined Jul 3, 2008
2,436
Please clarify. I see the rotation of the fields as opposite but I see the lines in between the conductors as going in the same direction as each other. My frame of reference needs adjusting.
Oh, yes, sorry about that. So the current directions are opposite and the circulation is opposite (clockwise and counter clockwise).

#12

#### PG1995

Joined Apr 15, 2011
816
Thank you very much, Steve. As always you have been great help.

So, in this post you did agree that the field lines won't cross. Now I also understand what t_n_k was suggesting. He actually wanted me to think in terms of superposition of the fields of both wires. Here I would like to quote one of my science teachers (not sure if he really was correct but so far it seems he is right). He used to say that many a time there are quite many differences between mathematical model and real physical model of a phenomenon. Still, mathematics helps us to reach the solution quite accurately because there is conformity and uniformity in mathematics' principles and as long as we stick to those principles the end solution would be right even though the actual phenomenon doesn't really work the way we have assumed in its mathematical world (quote ends here). For instance, here I believe we have the same situation. As you also agreed with me here that the fields won't mingle into each other but using superposition concept won't lead us to wrong result even though superposition does assume the field do mingle into each other. I hope you get my point.

steveb said:
For Q1, you are being asked to think in terms of superposition. The idea is that the net field can be equated to the sum of fields from individual pieces. When you think about the field of one piece, you have to mentally remove the other piece. You can't use the final solution, with the shown field lines, as a basis to say that the bottom part does not contribute fields to the upper part. So, even though the net field is zero (or small), the zero might be the result of a summation of nonzero things.
Q1: Here is my first follow-on question.

Now this is my follow-on question to this post.

steveb said:
...In this example, the combined effect of an infinite number of loops, spread out over distance, has the effect of rendering the loop radius unimportant for determining the field at the center...
Q2: Here is my question.

Best wishes
PG

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#### steveb

Joined Jul 3, 2008
2,436
OK, both questions seem to be related to the solution for the solenoid. I agree that the field is always small and never zero in reality. I also agree that the approximated formula for the field, is for the interior and not near the ends.

Essentially, the classical solution is an approximation and the approximation is made by considering the coil to be infinitely long, which is obviously can't be. So, there is always a fringe field near the ends and this loops back around the outside to allow the magnetic lines to make a complete circuit. Hence the fields near the ends do not obey the simple formula and the field outside can never be truly zero.

#### t_n_k

Joined Mar 6, 2009
5,447
Hi PG1995,

Regarding your virtual wall analogy in the diagram of post #12. This is where analogies start to break down. A current loop is a 3-dimensional entity. The field within the loop is radially symmetrical about the axis of symmetry and has the same value ( flux density) radially at any particular point and distance from the geometric center along the axis of symmetry [the NS line]. The radial value will of course vary as the field diverges or converges from point to point as one travels along the axis. The illusion created by the 2-D representation on paper leads you to propose a "wall" whereas what you must now propose is an infinitesimal [radius] line or filament of exclusion.
In addition one might be tempted to think that no flux can pass along the axis of symmetry by virtue of there being a notional barrier. In fact there is no impediment to flux existing along the line of symmetry.

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#### PG1995

Joined Apr 15, 2011
816
Hi PG1995,

Regarding your virtual wall analogy in the diagram of post #12. This is where analogies start to break down. A current loop is a 3-dimensional entity. The field within the loop is radially symmetrical about the axis of symmetry and has the same value ( flux density) radially at any particular point and distance from the geometric center along the axis of symmetry [the NS line]. The radial value will of course vary as the field diverges or converges from point to point as one travels along the axis. The illusion created by the 2-D representation on paper leads you to propose a "wall" whereas what you must now propose is an infinitesimal [radius] line or filament of exclusion.
In addition one might be tempted to think that no flux can pass along the axis of symmetry by virtue of there being a notional barrier. In fact there is no impediment to flux existing along the line of symmetry.
Thank you, t_n_k.

You are right. I do agree that the use of the word "wall" was a poor choice. Perhaps, saying that there exists a 'line-thick wall' along the axis of symmetry would have been more apt. Anyhow, thanks for pointing this out.

Best wishes
PG

#### PG1995

Joined Apr 15, 2011
816
Hi

I understand it's a long post and perhaps I should have made the queries in separate posts. But all three queries are related so I thought it would be a better idea to combine them in one post. It would be really kind of you if you could help me. Thank you for your time and help.

Magnetic field of an infinite straight current carrying conductor is given as: $$B=\frac{\mu _{0}I}{2\pi r}$$.

Likewise, electric field of an infinite line of charge is also given by a similar formula: $$E=\frac{\lambda }{2\pi \epsilon _{0}R}$$, "λ" is linear charge density, λ=Q/2a.

Magnetic field at the center of N circular loops is given as: $$B=\frac{\mu _{0}NI}{2a}$$, where "N" is number of loops and "a" is radius.

Q: Suppose we have a loop with an infinitesimal radius dr. It would be reasonable to assume that field over the cross section of the loop is constant, at least for the radius dr. The circumference of the loop is: 2π(dr). Assume that this circumference can be subdivided into infinitesimally small 10 segments, dl's, i.e. 10(dl)=2π(dr). When radius is double, the circumference gets doubled, i.e. circumference for 2dr radius=2π(2dr)=4π(dr). This means that dl segments carved out of the circumference also get doubled, i.e. 2(10)=20. This might lead one to erroneously conclude that magnetic field in the cross section of the loop is still constant because even though radius has been doubled but there have also been twice more segments to contribute to the field. But here one should consider the area of a circle which does have linear relationship with radius: area=πr^2. It means for each increase in radius area would increase more as compared to a simple linear relation. But still don't you think that the magnetic field at the very center of the loop should remain constant?

You can find Q1 and Q2 included in the attachment. I believe you would need to use high resolution copy of the attachment in this case therefore please use this link. If you can't see the image, then please use this username: imgshack4every1, and password: imgshack4every1.

Regards
PG

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