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 0.47 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 four, find the new value of the induced emf.

Explanation / Answer

According to the question we need to find the new value of the induced emf.

EMF = 0.47 V

Mutual inductance increases by a factor of 4 .

We know the formula for

(Emf) = - M*di1/dt =================================EQ(1)

As we cans see from the question itself mutual inductance increases by a factor of 4

So , the EMF increases by :

Induced (EMF) = 0.47 V * 4 = 1.88 V ========================ANSWER)

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