(Originais Teachy 2023) - Question Hard of Physics

A rectangular loop of conductor wire is placed in a uniform and constant magnetic field in such a way that the loop's area vector makes a 30-degree angle with the field lines. Initially, the magnetic flux through the loop is 0.03 T*m². The magnetic field is kept constant while the loop is rotated, so that after some time, the loop's area vector makes a 60-degree angle with the field lines. Considering that the magnetic field does not change during the rotation and that the sine of 30 degrees is 0.5 and the sine of 60 degrees is 0.87, answer: 1. What is the new value of the magnetic flux through the loop? 2. Is the change in magnetic flux positive or negative? Justify your answer based on the variation of the angle between the area vector and the field lines. Use the concepts of Faraday's Law of Electromagnetic Induction to support your explanation.