[toth]

>You can make the electric field disappear by choosing the right gauge. Same goes for the magnetic field (can't make both disappear together though).

What? No you can't. The fields are invariant under gauge transformations.

[ThePhysicist]

You're right, sorry I was thinking of a Lorentz transformation that would make either the magnetic or electric field disappear under certain conditions.

[wch4999]

"transform into each other" would be more appropriate. The gauge choice you mentioned is not totally wrong. The gauge freedom can be used to set the electric field to zero, but only once at a single point.

[toth]

Sorry, but gauge transformations do not (by construction) affect the physical fields at all. You cannot set E to 0, even at a point, with a gauge transformation.