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Homework Statement
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 25 m above the ground. The local power company tells you that the line operates a 12 kV and provide a maximum of 47 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.]
Homework Equations
[tex]
\\B = \frac{\mu_{0}I_{0}} {2 \Pi r}
[/tex]
[tex]
\\P_{max} = V_{0}I_{0}
[/tex]
[tex]
\\V_{0} = \sqrt{2}V_{rms}
[/tex]
The Attempt at a Solution
[tex]
\\V_{0} = 12000\sqrt{2} = 16970 V \\
[/tex]
[tex]
\\I_{0} = \frac{P_{max}}{V_{0}}= \frac{(47 * 10^6)}{16970} = 2769.6 A \\
[/tex]
Then, the current value is plugged into the equation of a magnetic field due to a wire with r equal to 25 m. All of this seems correct, but I continue to get the problem wrong. Does anyone see where I am tripping up here?
P.S. The very first equation is supposed to be divided by 2PIr, but I cannot get latex to show this for whatever reason...