In Figure 30-37 a 120-turn coil of radius 1.8 cm and resistance 5.1 a is coaxial

Question

In Figure 30-37 a 120-turn coil of radius 1.8 cm and resistance 5.1 a is coaxial with a solenoid with 239 turns/cm and diameter 3.2 cm (a) The solenoid current drops uniformly from 1.5 A to zero in time interval ? t 25 ms. What magnitude of current is induced in the coil during at? (b) Suppose instead that the solenoid current drops according to the function i 1.5e-80%, where t is in seconds and the current is in A. What is the magnitude of the initial induced current in the coil? (c) What are the units of the number 80 in the exponential? O S ?1/s O No units O A Solenoid Fig. 30-37

Explanation / Answer

Given,

N = 120 ; r = 1.8 cm ; R = 5.1 Ohm ; n/l = 239 turns/cm ; d = 3.2 cm => r = 1.6 cm = 0.016 m

a)I = 1.5 A ; I' = 0 ; t = 25 ms

We know that the B field of a solenoid is;

B = u0 n I

B = 4 pi x 10^-7 x 23900 I

B = 0.0300184 I T

we know from Faradays law

emf = N d(Phi)/dt = N A dB/dt

emf = 120 x 3.14 x 0.016^2 x 0.03 x 1.5/25 x 10^-3 = 0.174 V

i = V/R = 0.174/5.1 = 0.034 A

Hence, I = 0.034 A

b)di/dt = d(1.5 e^-80t)

di/dt = -80 x 1.5 x e^-80 t = -120 e^-80 t

for t = 0 ; di/dt = -120

emf = 120 x 3.14 x 0.016^2 x 0.03 x -120 = 0.347 V

I = 0.347/5.1 = 0.068 A

Hence, I = 0.068 A

c)it has units of

1/s

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