(Originais Teachy 2023) - Question Medium of Physics

A scientist is studying an ideal cylindrical solenoid, with all the turns very close together. The solenoid is 30 cm long, its inner radius measures 2 cm, and it has 300 turns. He wants to investigate the magnetic flux passing through the center of the solenoid over time. Knowing that the electric current passing through the solenoid is variable, the magnetic field intensity inside it varies according to the function B(t) = 2t² + 4t + 2 mT, where t is given in seconds. Considering π = 3.14, answer: a) Determine the mathematical expression of the solenoid's cross-sectional area. b) Calculate the magnetic flux that crosses the solenoid's cross-section at time t = 2 s. c) Verify if the magnetic flux is constant or varied at that moment in time.