Can Electric Fields Transform into Magnetic Fields in Different Inertial Frames?

[BMC]

Hey guys,

I couldn't find a question like this elsewhere on the forum so hopefully I'm not repeating what someone has already asked.

Can a purely electric field in one inertial frame of reference transform into a purely magnetic field in another? Explain

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My initial instinct was to say yes. Because if you're in the reference frame of the wave (i.e. you can't see the propagating electric field because you're moving with it), there's no subsequent magnetic field in your reference frame because the the electric field ins't changing with respect to time...

Then when you change your reference frame to not moving with the wave (you're stationary, watching the wave move past) you'd be able to see both the electric and magnetic field propagating because you'd be seeing the electric field changing with respect to time and the subsequent magnetic field being produced.

I however realized i wasn't reading the question correctly. It asks for a "pure" magnetic field and then a "pure" electric field upon a change of inertial reference frame.

Can anyone think of a situation where this happens?

 

[Count Iblis]

Intuitive reasonings can be misleading...

Hint: Can you think of a quantity that you can fom using E and B that stays invariant under Lorentz transforms?