Mutual induction can be used as the basis for a metal detector. A typical setup

Question

Mutual induction can be used as the basis for a metal detector. A typical setup uses two large coils that are parallel to each other and have a common axis. Because of mutual induction, the ac generator connected to the primary coil causes an emf of 0.42 V to be induced in the secondary coil. When someone without metal objects walks through the coils, the mutual inductance and, thus, the induced emf do not change much. But when a person carrying a handgun walks through, the mutual inductance increases. The change in emf can be used to trigger an alarm. If the mutual inductance increases by a factor of five, find the new value of the induced emf.

Explanation / Answer

as for M being the mutual inductance of the coils

induced voltage = rate of change in Flux*M

Now , as

Induced voltage is directly proporational to Mutual inductande

New Emf = 5 * 0.42

Emf = 2.1 V

the new value of the induced emf is 2.1 V

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