# Faraday's and Lenz law - Experiment with AC coil and Cu ring

• mik652
In summary: If you have a coil that produces a magnetic field, and you place a closed conducting loop of copper around the coil, called a "Faraday Cage," in the magnetic field the ring will be induced an electric current in such direction to opposes the magnetic field.
mik652
Hi,

can someone explain me the next experiment:

If I have an AC coil on iron stick, and if I put Cu ring on that stick concentric with AC coil, when I turn coil power supply, the ring will levitate on some height. My question is:

Powered AC coil produces an AC magnetic field. If I put a closed conducting loop (Cu ring) in that magnet field, in the ring will be induced current (Faradey law) in such direction to opposes magnetic field from AC coil (Lenz law). But in first quarter (N pole increasing) of sine wave of magnetic field from coil, the ring and and the coil will reject each other. In second and third quarter of a sine wave (N pole decreasing, and S pole increasing), the ring and the coil will attract each other. And in forth quarter of sine wave (S pole decreasing) the ring and the coil will reject each other again. Base on this I can conclude that the ring should stay in one position and should oscillate. Where is my mistake?
Maybe this is the answer (in first quarter, the ring is close to coil, and the reject force move coil on some distance. When force change its direction, inertia of the ring move the ring for a while and then starts to oscillate?

On the other hand if I draw the lines of forces that acts on ring, the are in such direction to tray to increase and decrease (depend from quarter of sine wave) the radius of the ring. The forces lines lie in ring surface.

Base on this if I put the same coil in the same magnetic field as described above, but in other position, so the magnetic field lines and the ring surface line are at 30 degrees, for example. Ring is fixed in its center, so it can only rotate, what will happen with ring. Will it rotates to position that surface line and magnetic field lines are at right angle, or to position where the angle between the lines are at 0 or 180 degrees? If we draw the lines of forces we can find that the ring will just oscillate in any position.

Where is my mistake in understanding of this situation?

Best regards

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mik652 said:
If I put a closed conducting loop (Cu ring) in that magnet field, in the ring will be induced current (Faradey law) in such direction to opposes magnetic field from AC coil (Lenz law).

Actually, it induces EMF which is equal to the rate of change of the magnetic flux enclosed by the loop. So, if your flux is proportional to ## sin(\omega t) ##, the induced EMF will be proportional to ## - cos(\omega t) ##. But a loop is an inductor with one turn and due to loop inductance, the induced current will be lagging the EMF and proportional to ## - cos(\omega t - \phi) ##. If the resistance of the loop is very small compared to its inductance, the lag angle ##\phi## will be close to 90 degrees and the induced current will be almost in phase with the primary magnetic field. That's what gives the repulsion.

Thanks for a replay, that's clear now, I have understand.
There is one more thing about electromagnetic forces between the ring and the coil. Let's say that I have DC power supply for a coil. When i turn on power supply i'll have increasing magnetic filed which will induce current in the ring. The induced magnetic field is in opposite direction of coil field. When I draw the lines of forces (Lorentz law), i can find that the ring shouldn't go from the coil but it want's to decrease its surface.
On the other hand, when I have, for example, N pole on coil and N pole on the ring, these two objects should reject each other, as experiment shows?
Can you draw me the lines of forces and explain me this situation?

Thanks

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you need to realize that induced emfs and induced currents oppose CHANGES in magnetic fields...not the same as opposing 'the field'...
You need to be comfortable with this otherwise you will often find that you get the opposite of what you expected.

Let's have a look at period while DC current is increasing (turning on DC power supply). The effect of that is increasing magnetic field. In this period the field is not constant, but increasing. In the ring will be induced increasing current in such direction to oppose the increasing field. For example, the coil in this period produce an increasing N pole up, the ring will also produce increasing N pole down to oppose coil field. When I draw the lines of forces, they acts in direction to decrease radius of the ring.
But when look logically if I have N pole on coil and N pole on a ring they should reject each other...But I can't find out how forces acts? It confuse me...

Mik652
My apology. After I replied to your post, I realized that I forgot to mention an important factor.
My first reply dealt only with time dependence. What I forgot to say was spatial dependence.
Your drawing is correct. If the field is uniform, you don't get a force on the ring to push it out, only the force that tries to squeeze the ring.
In real situation, the field is not uniform which means there will be a radial component to the field. And this field non-uniformity is what is needed to get a net force on the ring. I don't have a good drawing software, so I just added a few vectors to your drawing. It does show that you need a field non-uniformity to get the force on the ring.

## 1. What is Faraday's law and how does it relate to the experiment?

Faraday's law states that a changing magnetic field will induce a current in a conductor. In the experiment, the AC coil produces a changing magnetic field which induces a current in the Cu ring.

## 2. What is Lenz's law and how does it apply in this experiment?

Lenz's law states that the direction of the induced current will be in a direction that opposes the change in the magnetic field that caused it. In this experiment, the direction of the induced current in the Cu ring will be in the opposite direction of the changing magnetic field produced by the AC coil.

## 3. How does the number of turns in the AC coil affect the induced current in the Cu ring?

The number of turns in the AC coil affects the strength of the magnetic field produced, which in turn affects the magnitude of the induced current in the Cu ring. A higher number of turns will result in a stronger magnetic field and a larger induced current.

## 4. Why is a Cu ring commonly used in this experiment?

Copper is a good conductor of electricity and has low resistance, making it ideal for demonstrating the effects of Faraday's and Lenz's laws. It also has a high melting point, making it suitable for handling the heat generated by the induced current.

## 5. What other materials could be used in this experiment to demonstrate Faraday's and Lenz's laws?

Other materials that could be used include aluminum, gold, and silver, as they are also good conductors. However, the choice of material may affect the magnitude of the induced current due to differences in resistance and other properties.

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