You hold a metal ring horizontally above a bar magnet standing on its end. You drop the ring and catch it before it reaches the magnet. When, if ever, is a current induced in the ring?

Only when the ring stops falling

only when the ring starts falling

while the ring is falling

never, current is not induced

never, current is not induced

Explanation:

The induced emf in the ring equals the rate of change of magnetic flux in the ring.

E = -dФ/dt = -dAB/dt = -BdA/dt since B the magnetic field is constant.

E = -BdA/dt

Now dA/dt = dA/dy × dy/dt where dA/dy = rate of change of area with vertical distance as the ring is falling. dy/dt = speed of ring.

Since the ring is falling freely before being caught, its speed v is gotten from v = u + at where u = 0 and a = -g

v = 0 - gt = -gt

v = -gt  

So, dA/dt = dA/dy × dy/dt = vdA/dy = -gtdA/dy

So E = -BdA/dt = -B × -gtdA/dy = BgtdA/dy

Since dA/dy = 0 since the area of the ring does not change with vertical distance. So,

E = BgtdA/dy = Bgt × 0 = 0

E = 0

So, emf is never induced because the flux through the ring remains constant

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