Magnetic Field through moving circuit
Two conductive parallel rails are separated by a length of l = 1.2 m. On the left-hand side is a resistor running perpendicular between the two rails with a resistance of 6 Ohms. To the right is a metal bar connecting the rails (making a rectangular loop with the resistor). There is a magnetic field of 2.5 T directed into the page. How fast should the bar be moving to produce a current of .5 A in the resistor?
Answer
This is a classic Faraday's Law problem! Remember that the emf produced is the negative of changing magnetic flux with time. Start by writing the magnetic flux as the magnetic field times the area formed by the two rails, the resistor, and the metal bar. How can you find the change of this flux per time? One strategy is to write the position of the bar at time t = 0 as x_0, and the position at time t = Δt as x_0 + v * Δt. Then you can write the change in area ΔA = L * Δx. From here, divide by Δt and multiply by the magnetic field B to find the rate of change of the flux.
Now you should be equipped to find the emf and use Ohm's law to write the current in terms of the emf and the resistance. Finally, you can plug in all the numbers you have and solve for what you need.
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This is a classic Faraday's Law problem! Remember that the emf produced is the negative of changing magnetic flux with time. Start by writing the magnetic flux as the magnetic field times the area formed by the two rails, the resistor, and the metal bar. How can you find the change of this flux per time? One strategy is to write the position of the bar at time t = 0 as x_0, and the position at time t = Δt as x_0 + v * Δt. Then you can write the change in area ΔA = L * Δx. From here, divide by Δt and multiply by the magnetic field B to find the rate of change of the flux.
Now you should be equipped to find the emf and use Ohm's law to write the current in terms of the emf and the resistance. Finally, you can plug in all the numbers you have and solve for what you need.