Lenz’s Law – Wonder Tubes

Figure 1

Figure 1

Two similar looking cylinders, one magnetic and the other non-magnetic, are dropped down a long aluminum tube. The magnetic cylinder will fall much slower than the non-magnetic cylinder.

Materials:

  • Thin magnetic cylinder
  • Thin aluminum cylinder
  • A long aluminum or metal tube (not iron) with walls as thick as possible
  • One extra aluminum tube so that the magnetic and aluminum cylinders can “race” (optional)
  • Sand bag or soft surface for cylinders to land on
  • Rod and stand to hold aluminum tube upright

Demo:

Use the rod and stand to hold the aluminum tube(s) upright or simply hold over sand bags. First drop the aluminum cylinder into the tube and observe as it falls quickly under the force of gravity. Now drop the magnetic cylinder into the tube. The magnetic cylinder takes significantly longer to fall through the tube than the aluminum cylinder.

Explanation:

To understand what is happening in this process, let’s first examine Faraday’s Law of Induction. Faraday’s Law states that a change in the magnetic environment of a conductor will induce a current in the conductor. In our case, the changing magnetic field is a falling magnet which induces Eddy currents(also known as Foucault currents). Eddy currents are the circular currents induced in our aluminum tube by the change in magnetic field as the magnet falls.

What about these Eddy currents slows down the magnet as it falls? Lenz’s Law states that an induced current will flow to oppose the source which induced it. We can describe the induced electromagnetic field on our magnet mathematically using:

    • B = Magnetic field due to the Eddy Currents
    • A = Area of the aluminum tube
    • Φ = BA = Magnetic flux
    • n = Number of Eddy currents flowing through the aluminum tube
    • ΔΦ/Δt = Change in magnetic flux over time
    • emf = Electromagnetic field

With these definitions, the induced emf in our magnetic cylinder is:

emf = nΔΦ/Δt

Lenz’s Law states that an induced current will always flow in the opposite direction of that which produced it. In other words, the emf induced by the Eddy currents creates a magnetic field that opposes the magnetic field of the magnetic cylinder. This applies an upward force on the magnet that opposes the gravitational force downward, slowing down the magnet.

Figure 2

Figure 2

This new acceleration downward can be described by comparing the force of gravity to the magnetic force:

Fnet = Fmagnetic – Fgravity

Fnet = ma

a = Fnet/m

If we use an aluminum tube with thicker walls, the magnet will fall with an even slower acceleration. The magnetic field of the magnetic cylinder will create an emf over more area of the aluminum tube walls, hence creating a stronger force opposing the magnet.

If we drop the non-magnetic cylinder through the tube, no changing magnetic field exists and therefore no current or magnetic force is created and the cylinder remains unaffected.

Notes:

  • Stronger magnets and a tube with thicker walls can enhance the effects of the demo.
  • It is important to use sandbags or a soft surface for the magnet to land on, as it is prone to cracking.

Written by Lydia Seymour