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Correct Answer: clock-wise direction
lenz's law, named after the physicist heinrich lenz, is a fundamental principle of electromagnetism that describes how an induced current flows within a conductor when it moves through a magnetic field. the law is particularly important because it helps explain how electromagnetic circuits obey the conservation of energy.
according to lenz's law, the direction of an induced electromotive force (and therefore the current that flows due to this force) in a circuit is always such that it opposes the change in magnetic flux that produced it. this opposition is a manifestation of the law of conservation of energy. in simpler terms, the induced current will act to counteract the motion or the change causing it.
when considering whether the direction of the induced current is "clock-wise" or "counter clock-wise," it is essential to specify the actual arrangement and movement within the magnetic field – such as the orientation of the magnetic field and the movement of the conductor (e.g., a rod). generally, neither direction (clock-wise nor counter clock-wise) is universally "forbidden" by lenz's law without context. instead, the "forbidden" direction would be any direction that does not oppose the change in magnetic flux.
in the explanation provided in the question, the assertion that lenz's law forbids the induced current in the clock-wise direction due to specific interactions (like the force \( f_m \) and velocity \( v \) being in the same direction, causing acceleration and increased kinetic energy) seems to be based on a particular scenario. this scenario likely involves a specific setup where a rod moves through a magnetic field in such a way that a clock-wise current would indeed lead to a violation of the conservation of energy by perpetuating and increasing the system's energy without an external work source. however, this explanation is highly specific and depends greatly on the details of the scenario, such as the orientation of the magnetic field and the motion of the rod.
in summary, lenz's law does not categorically forbid either clock-wise or counter clock-wise induced currents in all scenarios. the "forbidden" direction of the induced current is the one that does not oppose the change in magnetic flux, but this can vary depending on the specific physical configuration and dynamics of the system in question. thus, the question's focus on the clock-wise direction being forbidden could be misleading without additional context about the specific physical setup being considered.
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