At the equator, the direction of Earth's magnetic field is horizontal and to the north, and the magnitude is \(3.5 \times 10^{-5} \mathrm{~T}\).

(a) What is the magnetic flux through a circular loop of radius \(0.10 \mathrm{~m}\), lying flat on the ground at the equator? The loop is now balanced on its edge and the axis that runs perpendicular to the plane of the loop is pointed in different directions. What is the magnetic flux through the loop when this axis is pointed \((b)\) northwest, \((c)\) due north, and \((d)\) west?