# Magnets down a copper tube and Lenz's law.

• georgebarnett
In summary, the conversation discusses the relationship between the number of magnets dropped as one body and the velocity at which it falls when dropped down a copper tube. The formula F = B^2VVol/ρ is used to calculate the force per magnet, with a factor of 70-80% efficiency due to field lines running in the air space. The electrical power generated in the tube is also calculated. The relationship between the number of magnets and the average velocity is shown in a table, and a theory about the changing shape of the magnetic field and its effect on the induced current is proposed.
georgebarnett
Right. I know if you drop a strong magnet down a copper tube (or conductive but non magnetic tube) it falls slowly as it 'sees' a changing magnetic field and thus induces a current in the tube and this induced current causes its own magnetic field to be induced and acts a resistive force to the falling magnet.

But I've been trying to work out how the number of magnets (dropped as one body) is related to the velocity at which it falls. Could anyone help me with this one? I've been trying to work it out for ages but can't seem to get very far with it.

Thanks in advance for any help!

I’ll see if I can help.
Say your copper tube has an inside radius R and wall thickness D. Suppose R>>D. Say the (average) length of the magnetic field lines outside the magnet is H. Strength of magnetic field is B.

Then starting with the upwards force F on the magnet exerted by the currents I flowing in the tube:

F=BIL (I don’t know the name of this formula).

Induced currents I are running in 2 circles along the circumference inside the tube. One clockwise say for the north pole and ccw for the south pole, depending on which way the magnet is turned. The current density J is I/A where area A=D x H.
Then I=JxDxH

L is along the direction of the current so here: L =2pi R.

Put this back in F. F=BxJxDxHx2pixR. Now call DxHx2piXR=Volume=Vol.
This is the effective volume of copper occupied by B.
So: F=BJVol
Now J=E/ρ where rho is resistivity of copper and E is the electric field generated by BxV of the falling magnet. J=BV/ρ

Hence: F=B^2VVol/ρ. This the force per magnet. If you bundle some N magnets close together then H is the length of each magnet and F is multiplied by N. Also factor in an efficiency in of perhaps 70 to 80% because of field lines running in the air space between magnet and tube.

The electrical power P generated in the tube is: P=FxV=(B^2V^2Vol/ρ)x%. You can check this out because P is also I^2 x resistance.
The resistance is 2pixRxρ/HD.

I’ve never done this experiment so let us know if my calculations make any sense.

This film confirms my calculations. Those small magnets can have magnetic B fields of up to 0.66 Tesla and with say a weight of 50 gram. If you put all that in the formula then V is very small say ~5 cm per sec.

Per Oni, thanks for you help. Your method makes sense but is not conclusive with my data. I think it may be easier if you see my data than me describing what I've found!

N V
1 0.568
2 0.279
3 0.269
4 0.264
5 0.318
6 0.370

N is the number of magnets, V is the average velocity (which equals terminal velocity - acceleration is negligible).

I think the relationship is to do with the changing shape of the magnetic field - with 3 or 4 magnets more of the field lines are perpendicular to the tube and thus a greater current is induced so a minimum terminal velocity is reached. What do you think?

## 1. How does Lenz's law relate to magnets down a copper tube?

Lenz's law states that when a conducting material, such as copper, experiences a changing magnetic field, an induced current will be produced in the opposite direction to the changing magnetic field. This means that when a magnet is dropped down a copper tube, the changing magnetic field will induce a current in the copper, creating an opposing magnetic field which will slow down the magnet's descent.

## 2. Why does the magnet slow down as it moves down the copper tube?

The induced current produced in the copper tube by Lenz's law creates an opposing magnetic field, which exerts a force on the magnet in the opposite direction to its motion. This force acts to slow down the magnet's descent, resulting in a slower overall movement.

## 3. Does the speed of the magnet affect the strength of the induced current?

Yes, the speed of the magnet does affect the strength of the induced current. According to Faraday's law of induction, the faster the magnet moves, the stronger the induced current will be. This is because the changing magnetic field is stronger when the magnet is moving at a faster speed.

## 4. Can Lenz's law be applied to other materials besides copper?

Yes, Lenz's law can be applied to any conducting material. However, the strength of the induced current and the resulting effects may vary depending on the properties of the material.

## 5. Is Lenz's law always present in the interaction between magnets and copper tubes?

Yes, Lenz's law is always present in this interaction as long as the magnet is in motion. This law is a fundamental principle of electromagnetism and applies to any situation involving a changing magnetic field and a conducting material, such as a copper tube.

• Electromagnetism
Replies
59
Views
4K
• Electromagnetism
Replies
5
Views
1K
• Electromagnetism
Replies
1
Views
976
• Electromagnetism
Replies
3
Views
1K
• Electromagnetism
Replies
2
Views
1K
• Electromagnetism
Replies
6
Views
1K
• Electromagnetism
Replies
3
Views
1K
• Electromagnetism
Replies
8
Views
1K
• Electromagnetism
Replies
27
Views
2K
• Electromagnetism
Replies
12
Views
2K