Question

Figure shows a magnet dropped through a small loop with a small cut. Which of the following statements is correct ?

• A. The speed of the falling magnet increases as it approaches the loop and starts decreasing as it crosses the loop.
• B. Acceleration of magnet increases as it approaches the loop and starts decreasing as it crosses the loop.
• C. Speed of magnet remains uniform as it moves through the loop.
• D. Acceleration of the magnet remains uniform as it moves through the loop.

Hint:

Always aggressively check the physical continuity of any loop in electromagnetic induction problems; an open loop generates EMF but definitively prevents any opposing force from manifesting.

Answer 1

The Correct Option is D

Concept:
• Faraday's Law of Electromagnetic Induction dictates that a changing magnetic flux seamlessly cutting through a wire loop will absolutely induce an electromotive force (EMF) across it.

• However, for this induced EMF to physically drive an actual induced electrical current, the loop must constitute a completely closed conductive electrical circuit.

• Lenz's Law further states that any induced current will flow in a specific direction such that its own generated magnetic field vigorously opposes the physical change in flux that fundamentally caused it.

• This magnetic opposition is what typically causes a falling magnet to perceptibly slow down when dropping through solid metallic rings or tubes.

Step 1: Analyze the physical geometry of the provided loop
The problem explicitly states and visually illustrates that the small loop possesses a "small cut".
This seemingly minor detail is profoundly important. A cut physically breaks the continuous electrical pathway.
Because the conductive pathway is broken, the loop inherently forms an "open circuit" with functionally infinite electrical resistance.

Step 2: Evaluate the electromagnetic induction effects
As the permanent magnet physically falls downwards due to gravity, the magnetic flux penetrating the area of the open loop genuinely changes over time.
Consequently, according to Faraday's law, a real electromotive force (EMF) is definitively induced strictly across the two ends of the small cut.
However, because the electrical circuit is permanently open, absolutely no induced electrical current can flow through the wire loop ($I = \frac{EMF}{\infty} = 0$).

Step 3: Determine the consequence of zero induced current
Lenz's law relies entirely on the presence of an induced current to generate a secondary opposing magnetic field.
Since there is zero induced current circulating in the open loop, there is absolutely no induced magnetic field created by the loop.
Consequently, the falling magnet experiences zero upward opposing electromagnetic force.
The only physical force acting on the magnet throughout its entire journey is the constant downward pull of Earth's gravity.

Step 4: Conclusion regarding kinematics
Because gravity is the sole force acting, the net force on the magnet strictly equals its weight ($F_{net} = mg$).
Using Newton's Second Law ($F = ma$), we see the downward acceleration of the magnet is precisely $a = g$.
Since the gravitational acceleration $g$ is practically a constant, the acceleration of the magnet remains completely uniform throughout its entire fall, regardless of its position relative to the cut loop.
This unyielding uniformity directly validates option (D) as the uniquely correct statement.