Animated Solution for Physics - Electromagnetic Induction: A coil is suspended in a uniform magnetic field with the plane of the coil parallel to the magnetic lines of force. When a current is passed through the coil, it starts oscillating; it is very difficult to stop. But, if an aluminium plate is placed near to the coil, it stops. This is due to

Understanding Electromagnetic Damping

Imagine you are pushing a child on a swing. If you stop pushing, the swing continues to oscillate for a long time because the friction from the air and the hinges is minimal. Now, imagine if you could stop that swing instantly without ever touching it. Sounds like magic, right? In the world of physics, this 'magic' is a very real phenomenon known as Electromagnetic Damping.

In our problem, we have a current-carrying coil suspended in a uniform magnetic field. Because it carries a current, it acts like a tiny magnetic dipole. When displaced, it experiences a restoring torque and begins to oscillate like a pendulum. Left to its own devices, it would swing for a very long time.

However, the plot thickens when we introduce an aluminium plate near the oscillating coil. Suddenly, the coil comes to a rapid halt. At first glance, this is baffling. Aluminium is a paramagnetic material—it is essentially non-magnetic in everyday situations. It doesn't attract the coil like a piece of iron would. So, what invisible hand is grabbing the coil?

Faraday's and Lenz's Laws

The secret lies in the dynamic relationship between electricity and magnetism. As the current-carrying coil swings, it carries its own magnetic field with it. When it moves closer to the aluminium plate, the magnetic field penetrating the plate increases. When it swings away, the field decreases.

This means the magnetic flux $\Phi$ linked with the aluminium plate is constantly changing over time. According to Faraday's Law of Induction, a changing magnetic flux induces an electromotive force (EMF), mathematically expressed as:

Because the aluminium plate is a solid block of conducting metal, this induced EMF doesn't just sit there; it drives swirling, whirlpool-like loops of electrical current within the bulk of the metal. We call these Eddy Currents.

The Opposing Force

Now, we must invoke the ultimate rule of cosmic karma in electromagnetism: Lenz's Law. Lenz's Law states that the direction of any induced effect will always oppose the change that caused it.

The 'cause' of the eddy currents is the physical swinging motion of the coil. Therefore, the eddy currents will circulate in a direction that generates their own magnetic field—a field specifically designed to repel the coil as it approaches and attract it as it tries to leave.

This creates a powerful magnetic drag force. The kinetic energy of the swinging coil is rapidly converted into electrical energy (the eddy currents) and then dissipated as heat within the aluminium plate due to its electrical resistance ($I^{2}R$ losses). The coil loses its energy and stops dead in its tracks. This beautiful, contactless braking mechanism is exactly what we call electromagnetic damping, making option (d) the perfect answer.