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A power line carrying a sinusoidally varying current with frequency f = 60 Hz and peak value I0 = 55 kA runs at a height of 7.0 m across a farmer’s land (Fig. 29–41). The farmer constructs a vertically oriented 2.0-m-high 10-turnrectangular wire coil below the power line. The farmer hopes to utilize the induced voltage in this coil to power 120-Volt electrical equipment, which requires a sinusoidally varying voltage with frequency and peak value V0 = 170V. What must the length l of the coil be?(Hint: Start with the magnetic field from the power line. Next, discover the flux in the loop. This requires integration because the magnetic field is not constant during the loop. Then use Faraday’s law with the flux to discover the induced EMF. You can then compute for the length.)
A sphere of radius R is uniformly charged to a total charge of Q. It is made to spin about an axis that passes through its center with an angular speed ω. Find the magnitude of the resulting magnetic field at the center of the sphere.
A resistor is in the shape of a cube, with each side of resistance R . Find the equivalent resistance between any two of its adjacent corners.
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