An attempt is made to elucidate the essence of relativistic length contraction by scrutinizing its various interpretations that appear in the literature.

The thread-between-spaceships problem is analysed both in its ‘mild’ variant (after some time the ships' acceleration ceases and they coast at the same constant speed, with respect to the lab frame), and in a special case of its ‘tough’ variant (the ships' acceleration never ceases). It is pointed out that in the special case of the tough variant the thread connecting spaceships may never break, regardless of how close the ships' speed approaches c.

Faraday's law for a filamentary circuit which is moving at relativistic velocities and also changing its shape as it moves is derived via the magnetic vector potential. The derivation is simpler than the usual one, based on the Hertz–Helmholtz identity.

The force exerted by a slowly moving current-carrying loop on a stationary or co-moving charge is derived within two distinct frameworks: Maxwell’s electrodynamics classically interpreted (operating in the Galilean space and time) and relativistic electrodynamics (operating in Minkowski space-time). A comparison between the ‘classical Maxwellian’ and relativistic solutions is presented, offering some intriguing insights that have been neglected in earlier discussions of the issue.

A curious property of the electrostatic image theory for the perfectly conducting prolate spheroid, introduced in 2001, is pointed out: the potential outside the conducting spheroid remains unchanged if the conductor is replaced by a dielectric spheroid with an embedded charge which coincides with the image charge for the conducting spheroid case. The present note is a generalization of the corresponding observation about the classical Kelvin image theory for the conducting sphere, made in 1988.