Final Answer:
The potential difference induced across the ends of the conducting rod moving at a constant velocity v in a magnetic field B is given by the formula V = Bvl, where V is the potential difference, B is the magnetic field strength, v is the velocity of the rod, and l is the length of the rod.
Step-by-step explanation:
According to Faraday's law of electromagnetic induction, the potential difference (V) induced across the ends of a conductor moving in a magnetic field is directly proportional to the magnetic field strength (B), the velocity of the conductor (v), and the length of the conductor (l). Mathematically, this relationship is expressed as V = Bvl.
The subscript/superscript style is used here to denote the variables: B for magnetic field strength, v for velocity, and l for length. The potential difference is calculated by multiplying these factors together.
In summary, as the conducting rod moves at a constant velocity in the magnetic field, the induced potential difference can be determined using Faraday's law, where the magnetic field strength, velocity, and length of the rod contribute to the overall induced voltage. The formula V = Bvl encapsulates this relationship.