Answer:
a) 
b) Length of the wire, l = 2.01 m
Explanation:
Number of turns, N = 99
diameter of the coil, d = 2.0 mm = 0.002 m
Area of the coil:
Time interval, t = 36 ms = 0.036 s
The fly turns through an angle of 90°
Magnitude of the magnetic field, B = 0.13 mT = 0.00013 T
From Faraday's law of Electromagnetism:

![\triangle \phi = BA [cos\phi_{2}) - cos\phi_{1}]\\\triangle \phi = (0.00013*0.00000314) [cos90 - cos0]\\ \triangle \phi = - 408.2 * 10^{-12} wb](https://tex.z-dn.net/?f=%5Ctriangle%20%5Cphi%20%3D%20BA%20%5Bcos%5Cphi_%7B2%7D%29%20-%20cos%5Cphi_%7B1%7D%5D%5C%5C%5Ctriangle%20%5Cphi%20%3D%20%280.00013%2A0.00000314%29%20%5Bcos90%20-%20cos0%5D%5C%5C%20%5Ctriangle%20%5Cphi%20%3D%20-%20408.2%20%2A%2010%5E%7B-12%7D%20wb)

2) The inductance of the inductor, L = 46.6 mH = 0.0466 H
Diameter of the copper wire, d = 3.29 * 10⁻² cm = 0.000329 m
Cross sectional radius of the tube, R = 2.53 cm = 0.0253 m
Area, A = πR² = π *0.0253² = 0.002 m²
For a closely packed layer, l = Nd
N = l/d
The inductance of the inductor can be given by the formula :

Length of the wire, l = 2.01 m