Answer
(a) Yes, we can conclude that the external electric field is also zero.
(b) No, we can't conclude that the external magnetic field is also zero.
Work Step by Step
The magnitude and direction of the velocity of the charged particle remain constant as it passes through a certain region of space. This implies that no external force is applied on the particle.
(a) If the external magnetic field is zero everywhere in this region, the external electric field has to be necessarily zero so that no external force is applied on the particle.
(b) If the external electric field is zero everywhere, the external magnetic field has not need to be necessarily zero because a charged particle does not experience any magnetic force, as it moves either parallel or anti-parallel to the magnetic field.
