You want to get an idea of the magnitude of magnetic fields produced by overhead

Question

You want to get an idea of the magnitude of magnetic fields produced by overhead power lines. You estimate that a transmission wire is about 16 m above the ground. The local power company tells you that the line operates a 18 kV and provide a maximum of 37 MW to the local area. Estimate the maximum magnetic field you might experience walking under such a power line, and compare to the Earth's field. [For an ac current, values are rms, and the magnetic field will be changing. Let the Earth's magnetic field strength be 5.0 10-5 T.]

I've tried using rms and max current... wrong answers include: 1.28E-5 T, 1.82E-5 T, 2.57E-5 T

Explanation / Answer

a) Irms =P/Vrms =(37*10^6)/(18*10^3)

Irms =2055.56 A

maximum current

Imax=sqrt(2)*Irms =2907 A

B=uo*I/2pir =(4pi*10^-7)*2907/(2pi*16)

B=3.634*10^-5 T

b)

B/Bmax =3.634*10^-5/(5*10^-5)

B/Bmax=72.67 %

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