Constants Part A A very long, straight solenoid with a cross-sectional area of 2

Question

Constants Part A A very long, straight solenoid with a cross-sectional area of 2.11 cm2 is wound with 88.7 turns of wire per centimeter. Starting att- o, the current in the solenoid is increasing according to i(t) 0.175 A/s2 )t2. A secondary winding of 5 tums encircles the solenoid at its center, such that the secondary winding has the same cross-sectional area as the solenoid. What is the magnitude of the emf induced in the secondary winding at the instant that the current in the solenoid is 3.2 A? Express your answer with the appropriate units. ???- 1 Value Units Submit Request Answer

Explanation / Answer

i(t) = (0.175 A/s^2)t^2

Given that -

n = 88.7 turns/cm = 8870 turns/metre

Now, the field inside the long solenoid is given by B = ??ni
B = 4?x10?? x 8870 x 0.175t² = 1.950 x 10?³ t²

dB/dt = 1.95 x 10?³ t

again -  

A = 2.11 cm² = 2.11 x10?? m²

|Emf| = rate of change of flux linkage

|Emf| = d(NAB)/dt = NA dB/dt
= 5 x 2.11x10?? x 1.95x10?³ t
= 2.057x10?? t

If T is the time at which the current = 3.2A
3.2 = 0.175T²
=> T = 4.28 s

therefore -  

|Emf| = 2.057x10?? T
= 2.057 x 10?? x4.28
= 8.80 x10^?6 V

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