Answer
See answers.
Work Step by Step
a. The magnetic field caused by the current in the power line points to the south at ground level beneath the wire, by the right hand rule.
Calculate the strength of this field. Use the formula for the magnetic field of a long, current-carrying straight wire.
$$B_{wire}=\frac{\mu_oI}{2\pi r}$$
$$ =\frac{4\pi\times10^{-7}(95A)}{2\pi(8.5m)}=2.2\times10^{-6}T $$
Compare the strength of this field to the Earth’s field.
$$\frac{B_{wire}}{B_{Earth}}=\frac{2.2\times10^{-6}T }{0.5\times10^{-4}T }=0.045$$
The strength of the field caused by the powerline is about 4.5 percent the strength of the Earth’s field.
b. Solve for the distance below the wire where the 2 fields have equal strength. Assume that the Earth’s field points due north so the power line’s field can cancel it.
$$B_{wire}=\frac{\mu_oI}{2\pi r}=B_{Earth}$$
$$r=\frac{\mu_oI}{2\pi B_{Earth}}$$
$$ r=\frac{4\pi\times10^{-7}(95A)}{2\pi(0.5\times10^{-4}T)}=0.38m $$
