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Why can't they meet or cut each other? I know magnetic field lines don't intersect with magnetic field lines and electric field lines don't intersect with electric field lines but why don't these intersect each other despite being of dissimilar nature?

Also do gravitational field lines also not interact with magnetic and electric field lines?

Aren't electric and magnetic fields in some sort of other planes or dimension? Because we can't feel them?

Karlo
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They can. See https://www.wyzant.com/resources/lessons/science/physics/magnetism

Electric fields are around charged objects. Most wires have equal numbers of electrons and protons. So they have no net charge and no electric field. But if they have extra electrons, they will have a charge. In the link, the picture of the wire shows the electric field when charges are sitting still.

Moving charges generate magnetic fields. In a wire, negatively charged electrons move and create a magnetic field. In most cases, positive nuclei pretty much stay still and don't generate significant magnetic fields. The picture shows the magnetic field of a steady current in a wire with no charge.

It is possible to have a current in a charged wire. You would see both electric and magnetic fields then. They would intersect.

You ask if field lines can cut or meet each other. You may be thinking of them as physical objects. They are not.

When you look at a topo map, you see lines of constant altitude drawn on them. Those lines are useful, and represent something physical. But when you walk around, you never see one. Magnetic and electric field lines are like that.

For completeness, I should mention some things I ignored above. Things get more complex when charges move in more complex ways. For example, electrons orbit nucei. Electrons and nuclei spin. Both of these generate magnetic fields. They are often small enough to ignore for everyday purposes. But not always. For example, this is the source of magnetic fields in permanent magnets. A full description requires quantum mechanics and relativity.

mmesser314
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    Electric fields can exist even in regions with zero net charge. Look at Jefimenko and a changing current. Magnetic field lines exist even when charges are stationary, consider the nonzero magnetic dipole moment of stationary electrons and protons. – Timaeus Mar 13 '16 at 17:10
  • @Timaeus - You are right of course. That wasn't clear in what I said? A charged wire will have an electric field whether or not the charges are moving. A wire with a current (electrons only moving) will have a magnetic field whether or not the wire is charged. – mmesser314 Mar 13 '16 at 18:53
  • It contradicts what you said, and experiments also contradict what you said. A wire that is net neutral can still have an electric field if it has a changing current, go look at Jefimenko's Equation. And you can also have a magnetic field even if every single charge in the universe is stationary. You claimed otherwise, so yes, the truth "isn't clear" when you state untruths. – Timaeus Mar 13 '16 at 19:01
  • @Timaeus - You got me. I was not paying attention. I was thinking in terms of electrostatics and steady currents. I was deliberately glossing over atomic structure and angular momentum, but that does introduce inaccuracies. I will add corrections and caveats. – mmesser314 Mar 13 '16 at 19:15
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I want to clarify something, since I think the other answers might be confusing the main point.

If you put down a million electric charges, move them around, etc, there will be a net magnetic field that is the sum of all the individual magnetic fields, and a net electric field that is the sum of all the individual electric fields. If you draw these field lines, they will not self-intersect. This is simply because at any given point, the net field can only point in one direction.

Now, if you just superimpose all the electric field lines of the individual charges, you'll get lots of intersections. But these intersections aren't "real"--the "real" electric field is the sum of all the individual electric fields, and the "real" electric field lines do NOT intersect.

EDIT in response to Timaeus

You get electric field lines by solving a parametric equations for curves $\vec{r}(s)$ satisfying $\vec{r}'(s) = \vec{E}(r)$. If we have a point where the electric field is zero, these curves never reach that point. For example, consider the case of two positive charges at $x=0$ and $x=1$. Along the x-axis, the electric field is given by

$$ E(x) = \frac{1}{x^2}-\frac{1}{(1-x)^2} $$

If we want to find the electric field line that goes across the x-axis, we need to find a solution for $x'(s) = E(x)$. If you plug that equation into WolframAlpha, you'll find that all the solutions asymtotically approach $x=\frac{1}{2}$ but never actually reach that point. Thus, there are no electric field lines at that point.

I believe this always is true, just because there are no nonconstant analytic functions that are constant on an interval. However, if you know a funny non-analytic counterexample, feel free to correct me.

Jahan Claes
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  • The zero field can point in many directions, that's why the field lines of the total field can (and do) intersect at places where the total feld is zero. – Timaeus Mar 13 '16 at 18:57
  • @Timaeus I feel it's more accurate to say that the electric field lines do not exist in regions where the total field is zero. This definition also matches with the way electric field lines are drawn. I understand you maybe want to let field lines intersect when there is just a single point where the electric field is zero, and you can extend the field lines continuously to cover this point. But you certainly don't want to say that you have electric field lines when you have an entire region with zero field. – Jahan Claes Mar 13 '16 at 20:27
  • @Timaeus See edit. – Jahan Claes Mar 13 '16 at 20:46
  • Your answer is horrible. Firstly, field lines can and do intersect and you claim they don't. Secondly, while I spend time explaining that field lines are not roads and things do not travel down them (energy actually flows orthogonal to electric field lines) you pretend that a fictional amount of time to travel down an instantaneous line somehow means something physical. The issue is that you if you pick a random point and find an integral curve through that point that is everywhere tangent to the instantaneous field values along the curve then far away it can hit a zero point. – Timaeus Mar 13 '16 at 20:59
  • So if you want to just not draw these points you have to know global properties to draw a field line just to avoid the fact that there really are integral curves that head to the same point and if you keep drawing them, the line in space goes straight from one charge to the other. But the directed line from one hits the directed line from the other where they ... intersect. But I'm also bothered by the false insinuation that I was talking about adjunct fields not the total field. That's not true. Ironically in electrostatics the adjunct fields do not cross themselves except at a source. – Timaeus Mar 13 '16 at 21:06
  • @Timaeus Please don't get defensive/hostile, I'm honestly not trying to attack you. I've always heard electric field lines to be DEFINED by solving the above parametric equation. And I've often heard it quoted that electric field lines never intersect. If you've heard an alternative definition, I would (really!) like to hear it. – Jahan Claes Mar 13 '16 at 21:32
  • @Timaeus (I think this is clearly a technical point, since we agree on the value of the electric field lines everywhere except a set of measure zero. But I'd still like to clear it up) – Jahan Claes Mar 13 '16 at 21:33
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    My 2 cents. There isn't much point to getting into the technicalities of corner cases. The broad intuitive picture is needed for this question. In that sense, Jahan Claes is for the most part right, but not completely. They only intersect at a point charge. But that is an important case. If you want to get technical, there are no point charges, 0 is a vector, and the electric field is 3 components of a tensor instead of a vector. None of those points clarify anything for a beginner. – mmesser314 Mar 14 '16 at 00:48
  • @mmesser314 Why would you claim they only intersect at point charges? If you have a sheet of negative surface charge density, then the fields lines on either side meet up (and they don't need infinite parameter to reach each other as if that has physical meaning). I don't see how it clarifies anything for a beginner if you pretend that when you sprinkle iron filings between two North poles that you don't actually see an obvious cross shape of two intersecting orthogonal lines. It is what you actually see after all. – Timaeus Mar 21 '16 at 07:34
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Electric and magnetic field lines can intersect with each other. As an example, put a capacitor inside a solenoid. But also, electric field lines can and do intersect each other. And even magnetic field lines can and do intersect each other.

For an example, place two equally strong magnets near each other and hold them and rotate them so their north poles point towards each other.

Now, in the place right in the middle between the two north poles, the magnetic field is zero.

And the field line pointing away from one north pole and the field line pointing away from the other north pole intersect right at that place where the magnetic field is zero.

The same exact thing happens if you hold two equal electric charges in place, the electric field halfway between them is zero. And the electric field lines intersect.

That said, fields lines are not roads and they are not cars. Nothing flows along them (despite us calling them lines of flux), so they aren't a road. And they don't move, so they aren't a car.

They are a graphical representation. The direction tells you the direction of the field at that point. And the density tells you the strength.

The reality is that every point in space has an electromagnetic field. And the electric part points in some direction and has a magnitude and the magnetic part points in some direction and has a magnitude.

We could draw a vector at every point. Or we could draw field lines. Those are both just pictures and each can be convenient at times.

does it mean that the place where electric field is zero there are no net electric field lines?

You have two magnetic field lines intersecting (one from each north pole) and with the direction of each one pointing in the opposite direction as each other (so both pointing towards the point of intersection). But you also have more field lines intersecting that point as well, whose directions go away from that point. If you want each field line to represent a fixed number of Webers then you need an equal number that point in as point out. They can also intersect at poles, but there as well, the same number are pointing out as pointing in, really you draw it as one curve that has another curve that touches it with them both going in the same direction where they touch. Like two circles that touch at a point.

For electric fields they can also intersect at places with charges, in which case they might all be pointing in or they might all be pointing out. So where a charge is located they point in different directions (just like for the zero field locations) but they could all point in or all point out (unlike the zero field location, or the magnetic pole).

Timaeus
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  • does it mean that the place where electric field is zero there are no net electric field lines? –  Mar 13 '16 at 17:11
  • @XBOveRLorD You have two field lines intersecting (one from each North pole) and with the direction of each one pointing in the opposite direction. But you also have more field lines intersecting as well, whose directions go away from that point. If you want each field line to represent a fixed number of Webers then you need an equal number that point in as point out. – Timaeus Mar 13 '16 at 17:17
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No vector field lines ever intersect. A vector field is a rule that assigns a unique vector to every point in space. If two field lines intersected, there would be no unique vector assigned to that point.

The above is also true when mixing different electric vector fields or different magnetic vector fields in the same space. Although they can illustrated on paper as different components of the actual total field the real resulting physical flux of the created Net field has one force vector per point in space.

In the case now of mixing electric with magnetic fields, say for example in right angles, the resulting net force vectors are the electromagnetic Lorentz force vectors which are also the only field vectors present physically in this case, in space.

So no, when combining static electric and magnetic fields there are no physically present separate electric and magnetic vectors occupying the same space with crossing flux but instead the electromagnetic Lorentz force vectors and the field is essentially a static electromagnetic field.

A material placed inside this static EM field, will experience both components of the EM Lorentz force:

$$ \mathbf{F}=q \mathbf{E}+q \mathbf{v} \times \mathbf{B} $$

but will move only in the direction of the Lorentz force vector $F$ (final trajectory will be combination with its initial velocity vector) which is the only physical field vector present for such a field. The component vectors $E$ and $B$ are only mathematical derivations of the mixed field.

Bottom line, static electric and magnetic flux lines cannot cross physically but instead combine and and transform to EM Lorentz force vectors thus static EM flux.

Markoul11
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