A magnet is moving towards a coil along its axis and the emf induced in the coil is ε. If the coil also starts moving towards the magnet with the same speed, the induced emf will be .

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(3) 2ε. Given: the magnet approaches the coil at speed v and induces ε; now the coil also moves towards the magnet at v. Idea: the induced emf is set by the rate of change of flux, |ε| = |(dΦ)/(dt)|, and that depends only on the relative motion of magnet and coil. At a given separation x: (dΦ)/(dt) = (dΦ)/(dx)·(dx)/(dt), where (dx)/(dt) is the speed at which the gap closes. Before: closing speed = v. After: closing speed = v + v = 2v. So at the same separation the flux changes twice as fast, and the induced emf becomes 2ε.

A magnet is moving towards a coil along its axis and the emf induced in the coil is ε. If the coil also starts moving towards the magnet with the same speed, the induced emf will be ______.

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