(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I tried to understand the problem b) and c).

2. Relevant equations

Faraday's law: ∇xE = - ∂B/∂t

emf ε = Bdv

Force : F =ma, Lorenz's force F=q(vxB) ==> ma = IdB

Power : power of battery = εI, mechanical power of the wire = Fv

3. The attempt at a solution

I think I solved a), where the magnetic force on the wire is F = IdB = ma and the speed v = at = IdBt/m.

I'm now tried to understand b) and c). First, I assume the initial speed is 0 at t=0 when the generator is replaced by a battery. The battery's power is εI, and it must be equal to the power consumed by the wire which is Fv = IdBv. Then the speed of the wire is v = ε/dB.

Also using Faraday's law I get to the same conclusion : ∇xE = - ∂B/∂t >>> ε = -∂(flux)/∂t = Bdv

It doesn't feel natural. The battery is connected at t=0, and in no time there the wire goes at speed v=ε/dB? So I think it is nonsense. But I don't know where I choose a wrong way. Help me plz.

I guess the answer to c) is that the current has to be 0, because when the terminal speed has been reached, there is no acceleration, then no force F=IdB=0. Am I right at this?

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# The speed of a metal wire on two rails with a magnetic field

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