Final answer:
In order to achieve zero induced emf while the rod moves to the right in a uniform magnetic field, the magnitude of the magnetic field should not change. This is because any change in the magnetic field would result in a changing magnetic flux, which by Faraday's law, induces an emf.
Step-by-step explanation:
The question involves a scenario where a conducting rod slides along metal rails in a uniform magnetic field, with a constant speed v, and asks for the condition under which the induced emf in the circuit would be zero. According to Faraday's law of induction, an emf is induced in the circuit when there is a change in magnetic flux. Since the rod is moving to the right and the area enclosed by the circuit is increasing, the flux through the circuit is increasing as well, implying that an emf is induced.
To ensure the induced emf is zero, we would need to counteract this change in flux. As the movement speed v and the length l of the rod are constants, and since the only other factor that would affect the magnetic flux is the magnetic field B itself, we would need to adjust the magnetic field. However, any non-zero, steady change in the magnetic field over time will continue to induce an emf, due to the changing magnetic flux. If the magnitude of the magnetic field B were to not change with time (remain constant), it would mean that the change in the area enclosed by the rod is the sole source of changing flux, and as long as the rod moves steady, a constant emf is induced. Hence, to achieve zero induced emf, the magnetic field should not change.