Q.At an airport, a person is made to walk through the doorway of a metal detector, for security reasons. If she/he is carrying anything made of metal, the metal detector emits a sound. On what principle does this detector work?

The doorway of the detector contains a coil that, together with a capacitor, forms an LC circuit driven near its resonant frequency $f_0=\dfrac{1}{2\pi\sqrt{LC}}$. At resonance the circuit carries a large, sharply-tuned current.

When a person carrying metal walks through, the metal alters the effective inductance of the coil, shifting the circuit away from resonance. This produces a marked change in the circuit's impedance and hence in its current. The electronics sense this change and trigg …

The archway you walk through is not a magnet — it is an AC circuit deliberately operated at resonance, exploiting how sensitively a resonant circuit responds to a small change in its components.

1. A tuned LC circuit

Built into the doorway is a coil (inductance $L$) connected with a capacitor (capacitance $C$) and driven by an oscillating source. Such a series circuit has a resonant frequency

at which the inductive and capacitive reactances cancel, the impedance drops to its minimum $Z=R$, and the current is at its sharp maximum. The circuit is set to run at (or very near) this resonant frequency.

2. Effect of a metal object

When a person carrying metal passes through the coil, the metal changes the magnetic environment of the coil and hence its effective inductance $L$. Because $f_0$ depends on $L$, the circuit is pushed away from resonance.

3. A large, detectable change …

Method: Electromagnetic Induction (Principle of Eddy Currents)

This is a concept-based reasoning method — no calculation is needed. The answer follows from understanding how changing magnetic fields induce currents in conductors.

Step 1 — Identify the core physical principle

The metal detector works on electromagnetic induction, specifically the production of eddy currents in a metal object.

Step 2 — Describe the setup

• The doorway contains coils that carry an alternating current (AC).
• This AC produces a changing magnetic field in the space around the doorway.

Step 3 — What happens when metal enters the field

• When a person carrying a metal object (conductor) walks through, the changing magnetic field induces circulating currents inside the metal.
• These are called eddy currents (by Faraday’s Law of Induction).

Step 4 — How the detector senses the metal

• The eddy currents themselves produce a secondary magnetic field.
• This secondary field is detected by receiver coils in the doorway. …

Here are the common mistakes students make on this question, along with the correct reasoning to avoid them.

Mistake #1: Saying it works on "Magnetic Effect of Current"

• The error: Students think the detector creates a magnetic field and if metal is present, it "attracts" the metal or somehow completes a circuit.
• Why it's wrong: The metal detector does not rely on magnetic attraction. It relies on a changing magnetic field inducing a current in the metal object.
• How to avoid: Remember: Static magnetic fields don't trigger the alarm. The field must be changing (alternating) to induce anything.

Mistake #2: Confusing it with "Electromagnetic Induction" in a transformer

• The error: Students write "mutual induction between two coils" but forget to mention the metal object acts as a secondary coil.
• Why it's wrong: In a transformer, both coils are fixed. Here, the metal object is the "secondary" — it has no wire attached.
• How to avoid: Say: "The metal object acts as a secondary coil in which eddy currents are induced."

Mistake #3: Forgetting to mention Eddy Currents

• The error: Students stop at "electromagnetic induction" without specifying that eddy currents are induced in the metal.
• Why it's wrong: The induced current in the metal is not a simple current in a wire — it's a loop of current (eddy current) inside the metal itself.
• How to avoid: Always include the phrase: "Eddy currents are induced in the metal object."

Mistake #4: Not explaining the detection mechanism

• The error: Students describe induction but don't explain how the detector knows metal is present.
• Why it's wrong: The induced eddy current in the metal creates its own magnetic field, which then induces a current back in the detector's coil — this change is detected.
• How to avoid: Add this step: "The eddy currents produce a secondary magnetic field, which induces a current in the detector's receiver coil, triggering the alarm."

Mistake #5: Writing the principle as "Lenz's Law" instead of "Electromagnetic Induction"

• The error: Students write "Lenz's Law" as the principle. …