Animated Solution for Physics - Electromagnetic Induction: Some laws/processes are given in Column I. Match these with the physical phenomena given in Column II.

Have you ever wondered how a simple ring can demonstrate the entire spectrum of Maxwell's equations? This matrix match question is a beautiful journey through electrostatics, magnetostatics, and electrodynamics. Let's break down each case and see how the physical phenomena unfold.

The Static Charge

Imagine a dielectric ring that is uniformly charged and completely at rest. Because the charges are stationary, there is no movement, and therefore, no electric current.

According to Coulomb's Law, these stationary charges will produce a time-independent electrostatic field in the surrounding space. Since there is no current, there is no magnetic field and no magnetic moment.

Thus, a static charged ring only produces an electrostatic field.

The Rotating Charge

Now, let's spin this charged dielectric ring with a constant angular velocity $\omega$. What changes?

First, the macroscopic charge distribution in space remains exactly the same. Therefore, the time-independent electrostatic field is still present.

However, the physical movement of the charges constitutes a steady electric current. A steady current loop generates a constant magnetic field and possesses a magnetic dipole moment.

So, a rotating charged ring gives us an electrostatic field, a magnetic field, and a magnetic moment!

The Steady Current

Next, consider a standard conducting ring carrying a constant direct current $i_0$.

A typical current-carrying wire is electrically neutral because the positive lattice ions balance the negative conduction electrons. Therefore, there is no electrostatic field outside the wire.

The steady current, however, produces a constant magnetic field and a steady magnetic moment. Because the magnetic field is constant, there is no changing magnetic flux, and hence, no induced electric field.

The Alternating Current

Finally, let's look at an alternating current in the ring, described by $i=i_0\cos \omega t$.

This time-varying current produces a time-varying magnetic field. This is where things get exciting! According to Faraday's Law of Electromagnetic Induction, a changing magnetic field creates a non-conservative, induced electric field in the surrounding space.

While this AC loop also has a time-varying magnetic moment, the most defining and unique phenomenon introduced in this case is the induced electric field. Therefore, we map it to the magnetic field and the induced electric field.

By simply changing the state of motion of charges—from rest, to steady rotation, to alternating flow—we transition seamlessly from electrostatics to magnetostatics, and finally to electrodynamics. This is the true elegance of physics!