Answer
See answers.
Work Step by Step
The fields created by the two wires, at the point indicated, will oppose each other.
The magnetic field caused by the downward-moving current points out of the page, by the right hand rule. Calculate the strength of this field by using the formula for the magnetic field of a long, current-carrying straight wire. The distance to the point from the center of the wire is 100 mm + 1.4 mm, from the picture provided with the problem.
$$B_{wire}=\frac{\mu_oI}{2\pi r}$$
$$ =\frac{4\pi\times10^{-7}(24.5A)}{2\pi(0.1014m)}=4.832\times10^{-5}T $$
The magnetic field caused by the upward-moving current points into the page, by the right hand rule. Calculate the strength of this field by using the formula for the magnetic field of a long, current-carrying straight wire. The distance to the point from the center of the wire is 100 mm - 1.4 mm, from the picture provided with the problem.
$$B_{wire}=\frac{\mu_oI}{2\pi r}$$
$$ =\frac{4\pi\times10^{-7}(24.5A)}{2\pi(0.0986m)}=4.970\times10^{-5}T $$
The net field points into the page, with a strength of $1.4\times10^{-6}T .$
Compare the strength of this field to the Earth’s field.
$$\frac{B_{wires}}{B_{Earth}}=\frac{1.376\times10^{-6}T }{0.5\times10^{-4}T }=0.028$$
The field is about 3 percent the strength of the Earth’s magnetic field.
