A power line carrying a sinusoidally varying current with frequency f=60 Hz and

Question

A power line carrying a sinusoidally varying current with frequency f=60 Hz and peak value I0=55kA runs at a height of 7.0m across a farmer's land. The farmer constructs a vertically orientated 2.0m high 10-turn rectangular wire coil below the power line. The farmer hopes to use the induced voltage in this coil to power 120-Volt electrical equipment, which requires a sinusoidally varying voltage with frequency f=60 Hz and peak value V0=170V. What should the length l of the coil be? Would this be unethical?

Explanation / Answer

Using Ampere's Law, we can calculate the magnetic field produced by the power line as

2 y B = u_0  I _0 sin( t)

B = (u_0  I_0 / 2 y) sin t

where y is the perpendicular distance from the power line to any point. The magnetic flux collected by the wire loop is then

= (u_0 L / 2 ) ln (y_2 /y_1 ) I_0 sin(t)

Given that y_1 = 5 and y_2 = 7 .

V = (u_0 L / 2 ) ln(y_2 /y_1 )   I_0 cos(t)

Solving for L we get

L = ( 2 V_0 / u_0 ln(y_2 /y_1 ) I_0 )

Substituting all the values to get solution          L = ............m

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