help please 2-Mutual induction can be used as the basis for a metal detector. A

Question

help please

2-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 0.49 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

4-You need to design a 60.0-Hz ac generator that has a maximum emf of 5315 V. The generator is to contain a 145-turn coil that has an area per turn of 0.90 m2. What should be the magnitude of the magnetic field in which the coil rotates?

Explanation / Answer

1) 2(60 Hz) 376.99 rad/s
d/dt (6.9e-5 T)(0.19 m^2)(376.99 rad/s)
Vp 1202 V
E = Nd/dt
N = E / d/dt
N (1202 V ) / [ (6.9e-5 T)(0.19 m^2)(376.99 rad/s) ]
N 34337 turns

2)  Emf2 = - M*di1/dt
so if M increases by 4 then emf increases by 4 so 0.49*4 = 1.96 V

3) EMF  induced in the 2nd coil = s = -M(Ip/t)

M = - s/(Ip/t) = 1.8/(-2.4/3.4*10^-2) = 0.0255 H

4) From Faraday's law,
V = N*d(BA)/dt = N*BA ==> B = V/(N*A)
= 2pi*60, A = 0.9, N = 145, V = 5315
B = 5315/(145*2pi*60*0.9) = 0.108 T

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