Workout Problem 4. A power line carrying a sinusoidal varying current with frequ

Question

Workout Problem 4. A power line carrying a sinusoidal varying current with frequency f- 60 Hz and a peak value of Lo 55kA runs at a height of 7.0 m across a farmer's land as shown in the figure below. The farmer constructs a vertically oriented 2.0-m-high 10-turn coil below the power line. The farmer hopes to use the induced voltage in this coil to power electrical equipment. Note 1(0)I, cos(o) 4-5%A " 60 H 1m Cell 20 m a. What is the magnetic field created by the power line? Leave it as a function of distance r, from the power line and time, t.

Explanation / Answer

a) at a distance r from the wire,

B = mue*I/(2*pi*r)

= mue*Io*cos(w*t)/(2*pi*r)

b) magnetic flux through the loop,

magnetic flux = integral N*B*dA

= integral (N*mue*Io*cos(w*t)/(2*pi*r))*l*dr

= (N*mue*Io*cos(w*t)*l/(2*pi)) integral (1/r)dr

= (N*mue*Io*cos(w*t)*l/(2*pi))*ln(r) (r valur from 5 to 7)

= (N*mue*Io*cos(w*t)*l/(2*pi))*ln(7/2)

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