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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

Respuesta :

oladayoademosu

Answer:

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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