Final answer:
The magnetic flux through a rectangle at the equator can be calculated as the product of the Earth's magnetic field strength, the area of the rectangle, and the cosine of the angle between the field and the area vector. Without the magnetic field strength provided in the question, we cannot determine the exact value of the magnetic flux.
Step-by-step explanation:
The magnetic flux through a rectangle laid out at the equator with an upward-facing area vector can be calculated using the formula for magnetic flux: Φ = B ⋅ A ⋅ cos(θ). Since the area vector is perpendicular to the ground and assuming a uniform magnetic field along the surface of the Earth at the equator, the angle (θ) is 0° (cos(0°) = 1).
To find the area (A) of the rectangle, we multiply its length by its width, A = 0.04m ⋅ 0.025m. The value of the Earth's magnetic field at the equator (β) is roughly 3.1×10⁻⁵ T. Therefore, the magnetic flux Φ through the rectangle is:
Φ = B ⋅ A ⋅ cos(θ) = 3.1×10⁻⁵ T ⋅ (0.04m ⋅ 0.025m) ⋅ 1 = 3.1×10⁻⁵ T ⋅ 1×10⁻³ m² = 3.1×10⁻⁸ Wb.
However, without the exact value of the Earth's magnetic field at the equator given in the question, we cannot select a precise answer from the options provided.