Animated Solution for Physics - Electromagnetic Induction: Assertion: A vertical iron rod has a coil of wire wound over it at the bottom end. An alternating current flows in the coil. There is a conducting ring round the rod as shown in the figure. The ring can float at a certain height above the coil. Reason: In the above situation, a current is induced in the ring which interacts with the horizontal component of the magnetic field to produce an average force in the upward direction.

Unraveling Thomson's Experiment

Imagine walking into a physics laboratory and seeing a solid metal ring levitating in mid-air above a simple iron rod. It looks like pure magic, but it is actually a beautiful demonstration of classical electromagnetism, famously known as Elihu Thomson's jumping ring experiment. Let's dive deep into the physics that makes this levitation possible.

The apparatus consists of a vertical iron rod with a coil of wire wrapped around its base. When we pass an alternating current (AC) through this coil, it acts as an electromagnet, generating a time-varying magnetic field $\vec{B}(t)$.

Because the coil is situated at the bottom of the rod, the magnetic field lines do not travel straight up perfectly parallel to the rod. Instead, they diverge as they move upwards and outwards into the surrounding space. This divergence is the critical secret to the levitation. If we examine the magnetic field exactly at the position of the floating ring, we find that the magnetic field vector $\vec{B}$ is tilted. It can be resolved into two distinct components: a vertical component ${\vec{B}}_V$ and a horizontal (or radial) component ${\vec{B}}_H$.

As the alternating current oscillates, the magnetic flux passing through the area of the conducting ring constantly changes. According to Faraday's Law of Induction, this changing magnetic flux induces an electromotive force (EMF) within the ring.

Consequently, an induced current $I_{ind}$ begins to flow through the ring. But in which direction? Lenz's Law tells us that the induced current will always flow in a direction that opposes the change in magnetic flux that created it. For instance, if the upward magnetic flux is increasing, the induced current will circulate in a way that generates its own downward magnetic field to fight the increase.

Now, we have a current-carrying ring sitting in a magnetic field. It will experience a magnetic Lorentz force given by the equation:

Let's analyze the interaction of the induced current with the two components of the magnetic field separately. The interaction between the induced current and the vertical component ${\vec{B}}_V$ produces a radial force. This force simply tries to compress or expand the ring horizontally, but it doesn't lift it.

The real magic lies in the horizontal component ${\vec{B}}_H$. If you apply the right-hand rule for the cross product $d\vec{l}\times {\vec{B}}_H$, you will find that the resulting force ${\vec{F}}_{up}$ points strictly upwards along the vertical axis!

You might wonder: since the current is alternating, shouldn't the force alternate between pushing up and pulling down, averaging out to zero? This is where the ring's self-inductance plays a heroic role. Because the ring has inductance, the induced current $I_{ind}$ lags behind the induced EMF. This crucial phase difference ensures that when you mathematically average the force over a full AC cycle, the upward pushes are stronger than the downward pulls. The result is a net time-averaged repulsive force pointing upwards.

This upward magnetic force constantly pushes the ring away from the coil. As the ring moves higher, the magnetic field gets weaker, and so does the upward force. Eventually, the ring reaches a specific height where this upward magnetic force perfectly balances the downward pull of gravity (the ring's weight, $m\vec{g}$).

At this exact sweet spot, the net force is zero, and the ring floats in stable equilibrium. Returning to our original question, the assertion that the ring floats is true, and the reason—that the induced current interacts with the horizontal component of the magnetic field to produce an upward force—is not only true but is the exact physical explanation for the phenomenon.