Magnetic Field due to Power Lines

[pssss]

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

$$\\B = \frac{\mu_{0}I_{0}} {2 \Pi r}$$
$$\\P_{max} = V_{0}I_{0}$$
$$\\V_{0} = \sqrt{2}V_{rms}$$

The Attempt at a Solution

$$\\V_{0} = 12000\sqrt{2} = 16970 V \\$$
$$\\I_{0} = \frac{P_{max}}{V_{0}}= \frac{(47 * 10^6)}{16970} = 2769.6 A \\$$

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...

 

[willem2]

I don't think they mean that P_max is the power delivered during the maximum voltage of an AC cycle. P_max is the rms power delivered during maximum load.

So $$P_{max} = 47 MW = V_{rms} * I_{rms}$$

Then $$I_0 = \sqrt {2} I_{rms}$$

 

[pssss]

Ahhhhh, okay. Yea, that fixed it. Thanks a lot!