A coil of 15 turns and radius 10.0 cm surrounds a long solenoid of radius 2.10 c

Question

A coil of 15 turns and radius 10.0 cm surrounds a long solenoid of radius 2.10 cm and 1.00X10^3 turns/meter (see figure below). The current in the solenoid changes as I = 4.00 sin 120 t, where I is in amperes and t is in seconds. Find the induced emf (in volts) in the 15-turn coil as a function of time.

A coil of 15 turns and radius 10.0 cm surrounds a long solenoid of radius 2.10 cm and 1.00 x 103 turns/meter (see figure below). The current in the solenoid changes as I = 4.00 sin 120 t, where I is in amperes and t is in seconds. Find the induced emf (in volts) in the 15-turn coil as a function of time 15-turn coil

Explanation / Answer

No of turns in the coil N(1) = 15
Radius r=0.1m
Area 'A' of the coil=pi*radius square=3.14*0.01=3.14*10^-2
current I =4.00sin(120t)
Rate of change of current=4*120 cos (120t )
Number of turns per unit length in solenoid n (2) =10^3turns/meter
Induced emf in the coil=d/dt N(1)*B*A=N(1)*permeability*n(2)*I * A
Induced emf in the coil=15*4pi*10^-7*10^3*rate of change of current*A
=60pi*10^-4*4*120cos120t *3.14*10^-2
v(t) =0.284 cos120t volt

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