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# How is it possible that the magnetic fields is perpendicular to the electric field?

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I recently learned in physics class that in an electromagnetic field, the magnetic field is always perpendicular to the electric field. But I don't under stand how that is possible, because the two fields are obviously both three dimensional. Geometry 101, it is not possible for two three dimensional entities to be truly perpendicular to each other unless there is a higher dimension involved.

At best, the only way to position two 3D entities perpendicular is to have a gap in between. How then are electromagnetic fields perpendicular?

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The magnetic field will not occur unless there is motion of the charge either spin or say linear motion. In terms of linear motion, this is one of the three x,y,z directions. The electric field, has a connection to a distinct force, with the field perpendicular to this. If I was to guess, the magnetic field is perpendicular to the electric field because it is a distinct force. If it was less than 90 degrees, it would merge with the electric field and not be a distinct force by become ambiguous. The direction of movement is perpendicular to both of these because it required another distinct force, not part of that charge, to get in motion. There may be some non-perpendicular overlap that is ambiguous leading to potential increase. What we see is the net affect that will make them all appear very distinct, minimizing potential.

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How can a vector be three-dimensional? It can only point in one direction at a time.

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Hypercube, think of vectors as arrows with a certain length and direction. Vectors being perpendicular is similar to toothpicks being perpendicular. The electric and magnetic fields are 3D vector fields, with each point in them a vector (sometimes they are drawn as lines, but it is more proper to draw them as arrows). The fields themselves are not perpendicular, but the vectors composing the fields are perpendicular. However, that is only true of induced electromagnetic fields.

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Actually, it is not generally true that E and B are perpendicular, even in induced fields. It _is_ true for the far field (self generating portion) of a plane E/M wave.

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I recently learned in physics class that in an electromagnetic field, the magnetic field is always perpendicular to the electric field. But I don't under stand how that is possible, because the two fields are obviously both three dimensional. Geometry 101, it is not possible for two three dimensional entities to be truly perpendicular to each other unless there is a higher dimension involved.

At best, the only way to position two 3D entities perpendicular is to have a gap in between. How then are electromagnetic fields perpendicular?

The perpendicularity isn't the right concept. An electric field is actually the same thing as a magnetic field, that's why we call it an electromagnetic field. The way it works is that if you move through an electric field, you would call it a magnetic field. Ditto if it's moving through you. A charged-up wire with no current flowing has an electric field. If there's a current flowing, the electric field is moving, so we call it a magnetic field. It's similar with a bar magnet, but instead of a current we've got electrons circulating in a favoured orientation.

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I think the OP was referring to an EM wave. Nevertheless, I think it reduces to a math concept of vectors and superposition; a vector at any point can only point in one direction, and the field at that point is the resultant of any fields that might be present.

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Yes, I imagine he was referring to this sort of thing:

Here the electric field is rising to the peak of the sine wave, and since it's a changing electric field it's also a magnetic field. But there is only one field, not two.

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An electric field is actually the same thing as a magnetic field, that's why we call it an electromagnetic field.

An electric field is not the "same thing" as a magnetic field. For instance, a constant uniform electric field can accelerate a stationary charge in a straight line. A constant uniform magnetic field can't do that.

The way it works is that if you move through an electric field, you would call it a magnetic field.

No, you wouldn't. You would see an electric field and a magnetic field. There is no way to start in a frame in which $|\vec{E}|\neq 0$, $|\vec{B}|=0$ and (Lorentz) boost to a frame in which $|\vec{E}^{\prime}|=0$ and $|\vec{B}^{\prime}|\neq 0$.

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Farsight, if you want to contradict established physics, please do so in Speculations. We're getting tired of this.

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It is actually the electricity flowing through a conductor that creates a magnetic field. It isn't really the same thing.

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