Three experiments that show Lenz at work

Three classic experiments make Lenz’s law visible and, at the same time, introduce induced currents in extended conducting masses.

(a) A magnet falling through a copper tube

A cylindrical magnet dropped through a non-ferromagnetic copper tube (pure copper!) takes many seconds to come out, against the fraction of a second predicted by free fall. As it descends, the flux through every cross-section of the tube changes: in the section below the magnet $\Phi_B$ is increasing, above it is decreasing. In the copper, induced current loops close up, producing magnetic fields that are always directed so as to oppose the magnet’s motion.

The descending magnet induces current loops in the copper (below and above itself), which generate a force $\vv{F}_\text{Lenz}$ directed upward, opposite to the velocity.

Within a few centimetres the magnet reaches a terminal velocity at which the weight $mg$ is balanced by the Lenz braking force, exactly as for a small ball in a viscous fluid. The force depends linearly on velocity (for small velocities), so $mg = b\,v_\text{lim}$ and the terminal velocity is

$v_\text{lim} = \frac{mg}{b}$

where $b$ gathers together all the geometry (conductivity, radii, magnetisation).

(b) Waltenhofen’s pendulum

A pendulum made of a copper disc swings between the pole pieces of a large electromagnet. With no current in the electromagnet the pendulum swings for a long time. As soon as we switch on $B$, the pendulum stops after one or two swings: the copper, sweeping through the field, sees $\Phi_B$ vary, and eddy currents flow within it that oppose the motion.

If we now take an identical disc but cut with radial slots, the currents can no longer close in a loop: the braking almost entirely disappears and the pendulum swings almost undisturbed. This is direct proof that what brakes it is not the copper as a material, but the possibility of closing a current loop inside it.

(c) The rock that behaves like a cat

We drop a small neodymium magnet onto a thick aluminium plate, from a height of about $30$ cm. It lands quickly but without bouncing and almost silently. Repeat it on an identical wooden block: a clean bounce. In the first instants of impact the magnet must displace the flux inside the aluminium, and Lenz opposes it: a sort of “magnetic shock absorber” with no moving parts.

Links

Topics: Electromagnetic induction Concepts: Lenz’s law · Eddy currents

Related exercises: Problem — The magnet in the copper tube · Worked exercise — magnet in a tube, terminal velocity · Magnet falling through a copper tube