Find speed of wire with voltage, length, and magnetic field

AI Thread Summary
A voltage of 1.50 V is induced in a 30.0 m wire moving perpendicularly through a magnetic field of 3.50×10–3 T, resulting in a calculated speed of 14.2 m/s. The discussion explores the forces acting on the charges within the wire, specifically the magnetic force (Fm) and the electric field (E) that counteracts it. The relationship between electric field and voltage is highlighted, suggesting that the voltage difference can be derived from the integral of the electric field over the wire's length. The user seeks to determine the electric field but struggles with the variables involved, particularly the charge (q) and its relation to the wire's length. The conversation emphasizes the interplay between voltage, magnetic fields, and the motion of the wire.
ettac
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Homework Statement


A voltage of 1.50 V is induced in a 30.0 m long wire as it moves perpendicularly to a 3.50× 10–3 T magnetic field. At what speed is the wire moving?
Answer is 14.2 m/s

Homework Equations


Fm=IlB
Fm=qvB
I=q/t

Thanks for all of your help! :)
 
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As the wire moves through the magnetic field, the charges inside feel a force of Fm=qvB. At equilibrium, this is counteracted by an electric field pushing the charges in the opposite direction. Can you find this electric field? If so, the voltage difference is just the integral of the field over the length of the wire.
 
I also have the formula Fe = Eq, but with that I do not know the E or the q.
I can go Fe = Fm , Eq=qvB, E=vB, v=E/B, v=Vq/B from there I don't know the q and I am not using the length of the wire (30.0m).
 
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