A power line carrying a sinusoidally varying current with a frequency of 60.0 Hz

Question

A power line carrying a sinusoidally varying current with a frequency of 60.0 Hz and a peak value of 75.0 kA runs at a height of7.0 m across a remote area of the country near a hermit's shack. The unscrupulous hermit plans to construct a vertically-oriented2.0-m-high rectangular wire coil below the power line; the coil will have 14 turns. The hermit hopes to use the induced voltage in the coil to power 240.0-volt electrical equipment; such equipment requires a sinusoidally varying voltage with a frequency of60.0 Hz and a maximum value of 339.4 V (the rms value times the square root of 2).

A power line carrying a sinusoidally varying current with a frequency of 60.0 Hz and a peak value of 75.0 kA runs at a height of 7.0 macross a remote area of the country near a hermit's shack. The unscrupulous hermit plans to construct a vertically-oriented 2.0-m-high rectangular wire coil below the power line; the coil will have 14 turns. The hermit hopes to use the induced voltage in the coil to power240.0-volt electrical equipment; such equipment requires a sinusoidally varying voltage with a frequency of 60.0 Hz and a maximum value of 339.4 V (the rms value times the square root of 2). What is the mutual inductance per unit length between the unscrupulous hermit's coil and the transmission line (i.e. per meter of coil length, where the coil length is expressed by the symbol l in the figure above). Give your answer in microhenries per meter. What is the required length l of the hermit's coil if he is to get the necessary peak voltage for operating his electrical equipment?

Explanation / Answer

a)0.2 mH

b)750 m

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