Part of JMAG-02 — Electromagnetic Induction & Lenz's Law

Rod on Rails — The Classic Setup

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A conducting rod slides on two parallel rails in a uniform field BB perpendicular to the rail plane. Key results: EMF =Bvl= Bvl, current =Bvl/(R+r)= Bvl/(R + r) where RR is external resistance and rr is rod resistance. The force F=BIlF = BIl opposes motion (Lenz's law). If the rod is given initial velocity v0v_0 and released: it decelerates exponentially v=v0eB2l2t/(mR)v = v_0 e^{-B^2l^2t/(mR)} with time constant τ=mR/(B2l2)\tau = mR/(B^2l^2). If pulled with constant velocity: the applied force equals the braking force. If pulled with constant force F0F_0: terminal velocity vt=F0R/(B2l2)v_t = F_0R/(B^2l^2).

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