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enter image description here

Considering the above diagram, I am failing to see why the aluminium ring floats upwards rather than oscillates. I understand Faraday's law, but I am struggling with Lenz's law - as there is an alternating current, an alternating magnetic field is produced, similar to a sine wave. Therefore, I assumed that the flux through the iron core can also be modeled as a sine wave, with the flux increasing and decreasing with the magnetic field.

As the flux increases through the ring, I understand that a current will be induced which opposes the increase in flux, i.e. a current which would produce a force upwards. However, in the case where the flux is decreasing i.e. from 90 to 180 degrees on a sine wave, it is my understanding that the ring will want to "increase" its flux, opposing this change and this would be a force downwards, rather than upwards so hence producing an oscillation.

However, I am given that "When the alternating current supply to the coil is switched on, the aluminium ring moves up the rod until it reaches a stable position ‘floating’ above the coil".

Can anybody shed any light on the situation?

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2 Answers 2

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This is a approximate answer but I think this could give some insight

Suppose the current is at the beginning of its sine wave and it is increasing (and without loss of generality suppose it is counterclockwise) then you would have a upward flux change so according to lenz law you would have a clockwise current in the ring. Magnetic field of the coil also have a (small) radial component which at the first half of period is outward. So because of this component there would be an upward force on the ring.

When it's a quarter into its period the flux change is downward but because of self inductance of ring it takes time to reverse the current in the ring.

After spending half the period the magnetic field of the coil is reversed and so its radial component (which is now inward). So the reversed current in the ring produces upward force again.

Fourth quarter is similar to the second one.

But the real picture is more complicated because speed of the ring also affects flux change (because the field decrease with height). But for a normal AC supply (50-60 Hz) current change should have a dominant effect.

So why it stops climbing? Because as the field weakens with height so is its rate of flux change and the induced current so there would be less force.

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  • $\begingroup$ Thanks for the answer. I was wondering if you could clarify what you meant by self inductance of the ring ? Thanks $\endgroup$ May 6, 2015 at 15:27
  • $\begingroup$ Every conductor that carries a current produces a magnetic field. When the current changes the magnetic field will change. This change of magnetic field causes a flux change in the conductor itself which induces a current in the conductor opposite to the direction of original change. So overall there would be less change in the current. The point here is that current in the ring is not exactly in phase with rate of current change in the coil. It lags. $\endgroup$
    – Azad
    May 6, 2015 at 15:41
  • $\begingroup$ If the current of the coil is sine, then in the absence of self-inductance current of the ring would have been a cosine. Radial component of mag field is also a sine. And the average of product of sine and cosine is zero over a period. But if you move the cosine slightly to right or left then it's nonzero. Self inductance causes that phase shift. $\endgroup$
    – Azad
    May 6, 2015 at 15:46
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The net force arises from the finite inductance and resistance in the ring. The induced current has phase lag relative to the induced voltage. Therefore, there is a time averaged net force. A very light ring might indeed show some 120Hz oscillations, if you could sense them.

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