WannabeNewton said:You're going to have to be way more detailed. I'm assuming ##E## and ##B## are the electric and magnetic field respectively. If so, then in general they are not orthogonal. For special solutions to Maxwell's equations they can be orthogonal, such as for vacuum radiation fields, but it is certainly not true in full generality.
WannabeNewton said:Have you seen vacuum plane wave solutions to Maxwell's equations before?
Orthogonal means that two vectors are perpendicular to each other. In the context of electromagnetism, it means that the electric and magnetic fields are at right angles to each other.
Proving that E and B are orthogonal is important because it is a fundamental principle in electromagnetism. It helps us understand the relationship between electric and magnetic fields and how they interact with each other.
The orthogonality of E and B can be demonstrated experimentally by using a device called a Faraday cage. This cage blocks external electric fields and allows for the measurement of the magnetic field perpendicular to the electric field inside the cage.
In theory, E and B should always be perfectly orthogonal to each other. However, in practical situations, there may be slight deviations due to factors such as the geometry of the setup or the presence of other electromagnetic fields.
Maxwell's equations, which describe the behavior of electric and magnetic fields, also show that E and B are orthogonal to each other. This relationship is known as the "curl-free" condition, which states that the curl of the electric field is equal to the negative of the time rate of change of the magnetic field, and vice versa.