A lighting flash is vertical and reaches a peak current of 1.50x10^5 amps in 5.0

Question

A lighting flash is vertical and reaches a peak current of 1.50x10^5 amps in 5.00x10^-6 seconds. An AM radio is located 15.0 km away. It has an antenna consiting 300 turns of wire, each with an area of 1.00cm^2. Assume that the magnetic field from the lighting flash is uniform over the area of the antenna coils and that it crosses the coils perpendiculary, maximizing the amount of magnetic flux through the antenna. What is the average voltage induced in the antenna as the lighting's current builds to its max value?

I NEED FULL EXPLANTION!!

A) 1.2V B) 6.0x10^-8V C) 0.012V D) 4.0x10-5 V

Explanation / Answer

i =1.5*10^5 A, t =5*10^-6 s, d =15 km , N =300 , A =1 cm^2

B = uoi/2pi*d = (2*10^-7*1.5*10^5)/(15000) =2*10^-6 T

from faradays law induced emf V = -d(phi)/dt = NAB/t

V = 300*1*10^-4*2*10^-6/(5*10^-6) = 0.012 V

Correct option is (C)

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