Final answer:
A stationary charge in front of a current-carrying wire does not experience a force from the electron current alone due to length contraction, because the relativistic effects are negligible and electric neutrality is maintained in the wire.
Step-by-step explanation:
When discussing a stationary charge in front of a current-carrying wire within the charge's frame of reference, where electrons flow and protons appear stationary, one might expect that the moving electrons undergo length contraction, as described by the theory of relativity. This would theoretically increase the electron density and cause a magnetic force on the charge.
However, the effects of relativity are generally negligible at the velocities electrons move in a wire compared to the speed of light. Moreover, the current in a wire consists of a drift of electrons with lots of collisions with atoms and other electrons, which doesn't create a significant net increase in charge density due to relativistic effects.
Moving charges experience a force in a magnetic field and generate a magnetic field themselves. However, in the situation described - where a stationary charge is placed near a current-carrying wire - what matters is the net electric field due to the charge distribution.
If there were a net change in electric charge density due to the motion of the electrons versus the protons, the stationary charge would indeed feel an electric force. But, due to the nature of the metal and the electrical neutrality maintained, no such net charge density change occurs, and thus, no electric force is exerted on the stationary charge by the current of electrons alone outside the wire.