A small bar magnet is moved through a coil at constant speed from one end to the other. Which of the

Q: Why is the deflection zero when the magnet is completely inside the coil?

When the magnet is fully inside, the magnetic field lines are entirely contained within the coil's cross-section. As it moves, the total number of field lines (magnetic flux) passing through the coil doesn't change. Since the rate of change of flux is zero, no EMF is induced.

Q: Does the speed of the magnet affect the galvanometer's deflection?

Yes! A faster-moving magnet causes a more rapid change in magnetic flux ($d\Phi/dt$), which induces a larger EMF and a greater deflection on the galvanometer. However, the *sequence* of directions remains the same.

Q: What if the magnet was inserted with the South pole first instead of the North pole?

The sequence of deflections would simply reverse. If it initially deflected left during entry, it would deflect right during exit. The key takeaway is that the entry and exit deflections are always in opposite directions.

Q: Why does the coil oppose the change in flux?

This is due to Lenz's Law, which is a consequence of the conservation of energy. If the induced current aided the change, it would create a runaway effect, generating infinite energy out of nowhere, which is physically impossible.

Q: Would a stationary magnet inside the coil induce any current?

No. A stationary magnet produces a constant magnetic flux. Without a *change* in flux over time, Faraday's Law dictates that the induced EMF is exactly zero.

Question

A small bar magnet is moved through a coil at constant speed from one end to the other. Which of the following series of observations will be seen on the galvanometer $G$ attached across the coil?

Three positions shown describe:
(i) the magnet's entery (ii) magnet is completely inside and (iii) magnet's exit.

Sigma Percentile · Accepted Answer

The phenomenon of electromagnetic induction is one of the most beautiful and symmetric principles in all of physics. When a magnet and a coil interact, they engage in a delicate dance governed by Faraday's and Lenz's Laws. Let's break down this classic problem step by step and understand exactly what the galvanometer is trying to tell us.

### Analyzing the Setup

Imagine you have a hollow coil of wire connected to a sensitive galvanometer. A galvanometer is simply a device that detects tiny electrical currents and shows their direction. Now, we take a small bar magnet and push it through the coil at a constant speed.

According to **Faraday's Law of Electromagnetic Induction**, an electromotive force (EMF) is induced in a circuit whenever there is a change in the magnetic flux linked with it. The magnitude of this induced EMF is directly proportional to the rate of change of magnetic flux:
$$ \varepsilon = - \frac{d\Phi}{dt} $$

The negative sign in this equation is crucial. It represents **Lenz's Law**, which states that the induced current will always flow in a direction that opposes the change in flux that produced it. With these two laws in our toolkit, let's track the magnet's journey.

### Phase (i): The Entry

As the magnet approaches and begins to enter the coil, the magnetic field lines piercing through the loops start to increase. The coil experiences a sudden surge in magnetic flux.

Because the flux is increasing ($d\Phi/dt > 0$), an EMF is generated to oppose this increase. The coil essentially tries to push the magnet away by creating its own magnetic field. This opposition causes a current to flow through the circuit, and the galvanometer pointer deflects to a particular direction. For the sake of our options, let's say it deflects to the **right**.

### Phase (ii): Completely Inside

Now, the magnet is completely swallowed by the coil. It is still moving at a constant speed, but we must ask ourselves: is the magnetic flux *changing*?

The answer is no. The total number of magnetic field lines linked with the coil remains constant as the magnet glides through the uniform central region. Since the rate of change of flux is zero ($d\Phi/dt = 0$), there is absolutely no induced EMF and, consequently, no current. The galvanometer pointer relaxes and drops back to **zero**.

### Phase (iii): The Exit

Finally, the magnet reaches the other end and starts exiting the coil. Now, the magnetic flux linked with the coil is rapidly decreasing.

Lenz's law kicks in once again! The coil doesn't want the flux to decrease, so it tries to pull the magnet back. To do this, it induces a current in the exact opposite direction compared to when the magnet was entering. Because the current has reversed, the galvanometer deflects in the opposite direction. Since it deflected right during entry, it must now deflect to the **left**.

### Final Conclusion

Putting it all together, the sequence of observations on the galvanometer is:
1. A deflection to one side during entry (**Right**).
2. No deflection when completely inside (**Zero**).
3. A deflection to the opposite side during exit (**Left**).

Looking at our given options, the visual sequence that perfectly illustrates this physical reality is **Option (b)**. The beauty of this problem lies in realizing that induction only cares about *change*, not just the presence of a magnetic field!

Select Answer:

Visualized Solution

$Faraday’s and Lenz’s Laws$

$Phase (i): Magnet Entering$

$Phase (ii): Magnet Completely Inside$

$Phase (iii): Magnet Exiting$

$Conclusion$

The Sigma Insight: Faraday's Laws of Electromagnetic Induction

Analyzing the Setup

Phase (i)

Phase (ii)

Phase (iii)

Final Conclusion

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