(Originais Teachy 2023) - Question Very Hard of Physics

A rectangular loop of 10 cm by 20 cm is placed in a uniform magnetic field of intensity 0.1 T. The loop is then tilted at 30 degrees with respect to the magnetic field, while keeping its orientation perpendicular to it. A student, when calculating the magnetic flux passing through the loop, considers only the projection of the loop's area in the direction of the magnetic field, omitting the inclination factor. Considering that the magnetic flux is given by Φ = B * A * cos(θ), where B is the magnetic field intensity, A is the loop's area, and θ is the angle between the magnetic field vector and the normal to the loop, calculate: 1) The correct value of the magnetic flux passing through the tilted loop. 2) The percentage loss when considering only the area projection and not the inclination factor. Explain, based on the involved physical concepts, how the loop's inclination affects the amount of magnetic flux that effectively passes through the loop.