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- Homework Statement
- In an inertial reference system ##S## there are an electric field ##\overline{E}## and a magnetic field ##\overline{B}##, uniform and constant, which form an angle ##\theta## with ##0<\theta<\frac \pi 2 ## between them.

1 - What completely general conclusions can be drawn about the fields ##\overline{E'}## and ##\overline{B'}##, seen in a generic inertial frame of reference ##S'##?

2- Calculate, if possibile, the speed ##\overline{v}## of the reference system ##S'## in which the fields are perpendicular. Justify the answer.

3- Calculate, if possible, the speed ##\overline{v}## of the inertial reference system in which the fields are parallel. Justify the answer.

- Relevant Equations
- Lorentz transformations

Good evening, I'm trying to solve this exercise that apparently seems trivial, but I wouldn't want to make mistakes, just trivial. Proceeding with the first point I wonder if my approach can be correct in describing this situation.

From the assumptions, the two fields are in this configuration:

I can observe that if the motion occurs along one of the two directions of the fields, in passing from one SRI to another, there will be a different value of the orthogonal component which it takes place in motion. If the motion occurs along the direction of the electric field, it will remain sent as it passes from one SRI to another. While the magnetic field will modify its orthogonal component to the electric field. In a similar way the vice versa holds true. In general, therefore, we can say that the components of the electric and magnetic fields parallel to the direction of motion will not undergo any change when passing from one SRI to another, while the orthogonal components will change. The inverse of what happened for the four-position and four-pulse occurs.

1 - What completely general conclusions can be drawn about the fields ##\overline{E'}## and ##\overline{B'}##, seen in a generic inertial frame of reference ##S'##?

From the assumptions, the two fields are in this configuration: