Answer:
[tex]1.74678 * 10^{-5}[/tex] T, up
Explanation:
If the height of power line, h = 60 m and distance between the power lines, d = 16 m, then we can use Pythagorean theorem to find the distance from power lines to the base, R.
[tex]R^2 = h^2+(d/2)^2\\\\R = \sqrt{h^2+(d/2)^2} = \sqrt{60^2+8^2} = 60.53[/tex] m
We need to find magnetic fields calculated from two current carrying wires and add them to find magnetic field at the base of the tower.
[tex]I(t) = I_0sin(2\pi f t)\\B(t) = B_{out}+B_{in}\\B_{out}(t) = \frac{\mu_0}{4\pi} \frac{2I_{out}(t)}{R} <cos\theta,sin\theta,0>\\B_{in}(t) = \frac{\mu_0}{4\pi} \frac{2I_{in}(t)}{R} <-cos\theta,sin\theta,0>[/tex]
Then,
[tex]B(t) = 2\frac{\mu_0}{4\pi} \frac{2I(t)}{R}sin\theta[/tex] in +y direction
Hence,
[tex]B = 2*\frac{4\pi * 10^{-7}}{4\pi}*\frac{2*2*10^4}{60.53}*\frac{8}{60.53} = 0.0000174678 = 1.74678 * 10^{-5}[/tex] T
The direction is +y, that is, up.
