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In essence, a metal detector utilizes principles of mutual induction to detect the presence of metal objects. Typically, metal detectors operate using two coils known as the primary and secondary coils. They are designed parallel to each other with a shared central axis. When a person walks through carrying a metal object, like a handgun, the metal influences the electromagnetic fields between the coils.
This happens because metal objects affect the magnetic coupling of the coils, altering the mutual inductance—how much the primary coil can induce a voltage in the secondary coil. As a result, the metal detector experiences a change in the induced electromotive force (emf), which can trigger an alarm. This is how even a small change in mutual inductance can play a crucial role in security and detection systems.

Electromotive force, commonly abbreviated as emf, is a core concept in electromagnetism. Essentially, it refers to the voltage generated due to a change in magnetic flux. In the case of the metal detector, the AC generator connected to the primary coil produces a fluctuating magnetic field, which in turn induces an emf in the secondary coil.
Emf is a critical parameter as it reflects how effectively the system can detect changes due to metallic objects. For example, in our scenario, an initial emf of 0.46 V is observed under normal conditions. This value gives a baseline from which changes, such as from encountering metal, can be measured.

Mutual inductance is the phenomenon where a change in electric current in one coil (the primary) induces an emf in the adjacent coil (the secondary). This concept is fundamentally related to metal detectors. When mutual inductance increases, so does the induced emf in the secondary coil. A change in mutual inductance occurs when the magnetic environment of the coils changes, such as when metal is near the coils.
In practice, this means that when the mutual inductance between the coils increases by a factor, the induced emf will increase by the same factor. Hence, a three-fold increase in mutual inductance leads to a new induced emf that is three times the original, perfectly illustrating the direct relationship between mutual inductance and induced emf.

An AC generator plays a significant role in systems like metal detectors through its ability to produce alternating current. This AC current creates changing magnetic fields which are crucial in inducing emf in the secondary coil of the detector.
The alternating nature of the current causes continual changes in magnetic flux, making it vital for detecting the presence of metallic objects. Without the AC generator, the metal detector would not have the fluctuating magnetic field necessary for mutual induction to operate effectively. Essentially, the AC generator is what powers and drives the induction process at the heart of detection technology.