The potential difference across the two ends is given by

Where is the emf or potential difference

v→ velocity of conducting rod

B is the magnetic field

L is the length of the rod

Consider some conditions,

i. The magnetic field is in the perpendicular direction to the velocity of the rod

ii. The magnetic field is in the perpendicular direction to the length of the rod

iii. The velocity of the rod is perpendicular to the direction to the length of the rod

In the above-mentioned conditions, only the potential difference across the two ends will be non zero.

In the given conditions in the A, B and C, the potential difference across the two ends is zero. So option D is correct.