Final answer:
To calculate the magnetic flux through the coil, you need to multiply the magnetic field strength by the area of the coil and the cosine of the angle between the magnetic field and the normal to the coil's surface. The area is found using the radius given, and in this case, the cosine of the angle is assumed to be 1 since the angle is not provided. An error in the calculation suggests a recalculation or revision of the concept.
Step-by-step explanation:
The student's question pertains to calculating the magnetic flux Φ through a circular coil with a given number of turns, radius, and magnetic field strength. The formula to use for the magnetic flux (Φ) through a coil is Φ = B ⋅ A ⋅ cos(θ), where B is the magnetic field strength, A is the area of the coil, and θ is the angle between the field lines and the normal (perpendicular) to the coil's surface. Here, since θ is not provided, we can assume that the field is perpendicular to the coil, making cos(θ) = 1.
First, we need to calculate the area A of the coil using the formula A = π ⋅ r², where r is the radius of the coil. With a radius of 12.0 cm (0.12 m), A = π ⋅ (0.12 m)² = 0.0452 m². Now, we can calculate the magnetic flux through the coil as Φ = 0.0670 T ⋅ 0.0452 m², giving us Φ = 0.00302 T⋅m² because the question asks for the magnitude, the effect of 300 turns does not need to be factored into the calculation.
The correct answer that matches the options is not present, hinting at a possible error in the calculation or understanding of the concept; therefore, the answer should be recalculated or the premise revisited.