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A coil of 15 turns and radius 10.0 cm surrounds a long solenoid of radius 1.70 cm

A coil of 15 turns and radius 10.0 cm surrounds a long solenoid of radius 1.70 cm and 1.00 × 10³ turns/meter (see figure below). The current in the solenoid changes as I=5.00 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.


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Answer #1

The magnetic field generated by the solenoid is given by

Β = μ.nl

n = number of turns per unit length = 1000

I = 5sin(120t) given

по = 4л х 10-7

Magnetic flux is given by

o = BA

A is area of solenoid

By Faradays law

V = no

N = 15

now substituting all the above values we get

dB V = 15AB = 15(1 * 0.0172)(4,1000)

V = 0.1711 x 10-4(5 x 120 x cos(1200))

V = 0.0102 x cos(1200)

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