# Two possible directions of the B field in relation to the E field in radio waves. How induce the left-handed direction?

In vacuum the two field components of a radio wave are directed perpendicular on each over. $$\mathbf{E}$$, $$\mathbf{B}$$ and $$\mathbf{k}$$ form a right hand system ($$\mathbf{k}$$ is the direction of propagation).

Source

This matches the right hand rule for a current carrying wire and the induces magnetic field around the wire.

Now, for the reasons of symmetry, a radio wave also could be drawn with $$\mathbf{E}$$, $$\mathbf{-B}$$ and $$\mathbf{k}$$. Aplicated to the image above, the green fieldlines (which showing the direction of the magnetic field) simply would show in the opposite direction. How induce a left hand radio wave?

• left-handed meta materials do just that. They are the topic of much current research. – garyp Feb 16 at 14:30
• Closely related question by the same user: physics.stackexchange.com/q/461167/44126 – rob Feb 16 at 15:25

If you change $$\overrightarrow{B}\to -\overrightarrow{B}$$ and $$\overrightarrow{E}\to \overrightarrow{E}$$ the Maxwell Faraday equation $$\overrightarrow{\nabla }\wedge \overrightarrow{E}=-\frac{\partial \overrightarrow{B}}{\partial t}$$ would not be true anymore.