# Is there any example where electric and magnetic fields are not perpendicular?

Perpendicular electric and magnetic field creates light or other electromagnetic waves. Is it a necessary property to have a perpendicular fields? If not what would happen when the fields are not perpendicular?

• A moving electric field, creates the perpendicular magnetic field. Apr 14, 2013 at 19:36
• @KaziarafatAhmed: Yes there is! In wave guides there modes of propagation. What we know as transverse electromagnetic field is just the TEM mode of a field. There are also the TE(transverse electric mode) with $B_z\neq 0$ and the TM(transverse Magnetic mode) with $E_Z\neq 0$ where $z$ is the direction of propagation! Apr 18, 2013 at 12:33
• Just put a charge at rest in a magnetic field. The Coulomb field goes out in all directions, and will cross the magnetic field at every possible angle. Nothing special happens. Apr 18, 2013 at 12:44
• please note that if $\vec{E} \vec{B}$ is not equal to $0$, i.e. fields are not perpendicular, then there always exist a reference frame where $\vec{E}$ is parallel to $\vec{B}$. In particular, this is the case of neutrino field. Apr 18, 2013 at 14:54
• @MurodAbdukhakimov: if ... fields are not perpendicular, then there always exist a reference frame where E is parallel to B Not true. The quantity $E\cdot B$ is a relativistic invariant. See en.wikipedia.org/wiki/…
– user4552
Aug 17, 2013 at 18:29

Yes there is! In wave guides, there are modes of propagation. What we know as transverse electromagnetic field is just the $TEM$ mode of a field. There are also the $TE$ (transverse electric mode) with $E_z≠0$ and the $TM$ (transverse Magnetic mode) with $B_z≠0$ where $z$ is the direction of propagation!

• But there you are talking about the multipole expansion of the EM-field (in Classical ED it might be not very explicit, but it is there). The fields still stay perpendicular to each other locally. Longitudinal components come from working with a spherical wavefront in cartesian basis, from what I understand. If this is not convincing, take Maxwell's equations in free space, go to reciprocal space and you will see that you NEVER can have a longitudinal component in absence of sources. Aug 3, 2017 at 20:36

1) It is necessary for a plane EM wave. If one assumes solutions to the Maxwell's equation to be plane waves, it is not hard to show that $\vec B \cdot \vec E = 0$.

Namely, take the third Maxwell's equation and dot both sides with $\vec E$.

$$\nabla \times \vec E = - {{\partial \vec B} \over {\partial t}}$$ $$i\vec k \times \vec E = i\omega \vec B{\rm{ }}$$ $$(\vec k \times \vec E) \cdot \vec E = \omega \vec B \cdot \vec E$$ $$0 = \vec B \cdot \vec E$$ 2) In general case, it is not necessary.

Assume a constant current flowing up along the z axis. It produces static magnetic field around it in the form of concentric circles (and no electric field as net charge inside the conductor is zero).

Put a positive charge to a point (-1,0,0). It produces static electric field with radially outward lines.

At the point (0,1,0) the angle between electric and magnetic fields is 45 degrees. Electricity can be static, like the energy that can make your hair stand on end. Magnetism can also be static, as it is in a refrigerator magnet. A changing magnetic field will induce a changing electric field and vice-versa—the two are linked. These changing fields form electromagnetic waves. Electromagnetic waves are formed by the vibrations of electric and magnetic fields. These fields are perpendicular to one another in the direction the wave is travelling. Once formed, this energy travels at the speed of light until further interaction with matter.

Maxwell developed a scientific theory to explain electromagnetic waves. He noticed that electrical fields and magnetic fields can couple together to form electromagnetic waves. The terms light, electromagnetic waves, and radiation all refer to the same physical phenomenon: electromagnetic energy. This energy can be described by frequency, wavelength, or energy. All three are related mathematically such that if you know one, you can calculate the other two. There’s a particle model and a wave model for electromagnetic radiation, and as we know electromagnetic radiation have dual nature. For an electromagnetic radiation to persist the two electric and magnetic fields have to propagate in a perpendicular direction to each other, EM waves consist of oscillating electric and magnetic fields.

• This doesn't really address the question of whether or not E and B fields can be non-perpendicular. It only states that the fields can only be perpendicular for EM radiation, which is misleading because there are situations in which you can have E and B fields that are not perpendicular
– Jim
Sep 15, 2014 at 18:09
• I don't think you read my question carefully. @hariom Sep 15, 2014 at 18:17

According to my understanding at physics, an electric field which is static cannot create any magnetic field.According to faraday for a magnetic field to exist there should be a varying electric filed(which varies over time).A simple example is battery connected to coil which is moved in and out near the galvanometer shows deflection(A galvanometer is device which detects magnetic filed by coupling magnetic filed near its vicinity to the coil inside and it internally has magnet which orients along the direction of earths's.The needle which is connected the coil coupling the magnetic field experiences a torque due to the EMF induced in it,and rests in the direction such that the earths magnetic field and the coupled magnetic are perpendicular to each other..hence the deflection of the galvanometer needle shows the stregth of magnetic field.

• According to faraday for a magnetic field to exist there should be a varying electric filed(which varies over time). No. This is only one of the two source terms for magnetic fields in Maxwell's equations.
– user4552
Aug 17, 2013 at 18:31