Final answer:
The magnitude of the force required to pull the rod at a constant speed v is F = Bv/R.
Step-by-step explanation:
The magnitude of the force that must be applied by a person to pull the rod to the right at a constant speed v is given by the equation F = Bv/R. This means that the force required is directly proportional to the magnetic field strength B and the velocity v, and inversely proportional to the resistance R of the rod. Therefore, the correct answer is F = Bv/R (option c). When the rod moves through the magnetic field, it experiences a change in magnetic flux, which, according to Faraday's law of induction, induces an electromotive force (emf). The magnitude of the induced emf, ε, can be calculated using ε = Bvl, where B is the magnetic field strength, v is the rod's velocity, and l is the distance between the rails. Ohm's law, which states that the current I equals the emf divided by the resistance R (ε = IR), can be used to find the current in the circuit induced by the motion of the rod. Once we know the current, we can calculate the magnetic force on the rod due to the current carrying conductor in the magnetic field, which is F = BIl. Because the rod moves at a constant speed, the net force on it must be zero. Therefore, the applied force must be equal and opposite to the magnetic force.