Electromagnetic Surge on Conductor

The voltage potential is the same at both ends making the assumption that the wire and ground are perfect conductors, which blows the whole thing out of the water anyway.

Homework problems like this frequently do not represent the real world.

The voltage is going to be expressed as a function of the magnetic field strength at the wire. Read your text book and do your own homework.

You have an odd way of asking others to do your homework for you.

An electric field pulse would cause a->b and c->d to be in phase. A magnetic pulse would cause a->b and c->d to be in opposite phase. It depends on the conditions like the orientation of the pulse and the size and geometry of the conductors, and most likely they would be neither in phase nor of opposite phase but would be different waveforms.

As postulated, the potential relative to ground at points a and c are zero just before the pulse is applied therefore they are zero at the instant the pulse is applied since nothing in nature changes in zero time. The pulse then splits and travels at the speed of propagation along the conductor in both directions at the same rate until it reaches points a and c, at which time the voltage appears with a fast rise-time. Since this is an unterminated transmission line the pulse will be reflected back to its origin and the cycle repeats until all the energy dissipates. Of course the same is true for the pulse traveling in the opposite direction. Transient analysis is different than steady state analysis.