Question

Any ideas. I'm stuck and need help

A 20Ohm coil of 15 turns and radius 10.0 cm surrounds a long solenoid of radius 5.0 cm and 1000 turns/meter (see figure below). The current in the solenoid changes as I = b sin (a t), where I is in amperes and t is in seconds. Let a = 120 rad/s and b = 6 A. What is the magnitude of the EMF in the 15-turn coil as a function of time? What is the magnitude of the EMF at 3 seconds? Be sure to show all parts of a physics problem for credit.

Answer 1

Ans :- here R = 10cm N= 15 turns ; r = 5cm; n= 1000; I= 6 sin(120t)

Because the solenoid is long, we can pretend it is infinite, so all the magnetic field is contained inside the solenoid, and there is no magnetic field outside

The field inside the solenoid is given by

B = µ0nI ...........................1

So the flux through the large coil is

Φ_B = ᶴ BdA = Nπr^2B = Nπr^2 µ0nI........................2

The induced emf is then

ε = − dΦ_B/ dt = −πµ0nNr2 dI /dt =- 3.14*4*3.14*10^-7*1000*15*(0.05)^2*6*120*cos(120t)

ε =106.48cos(120t)mV

t=3s

ε= 106.48mV