(Originais Teachy 2023) - Question Medium of Physics

In a futuristic city, a team of engineers is designing a magnetic levitation-based transportation system. They have at their disposal a coil with cylindrical coordinates that can be used in the project. The coil has a radius R and a length L and is wound with copper wires, with N turns per unit length. When an electric current I flows through the coil, it produces a magnetic field B inside it. We would like to calculate the intensity of the magnetic field generated by this coil that will be used in transportation. To do this, (a) deduce the expression of the magnetic field (B) on the central axis of the coil and (b) find the intensity of the magnetic field generated by the coil when: R = 0.1 m, L = 1 m, N = 1000 turns/m, and I = 10 A. (c) If we want to increase the magnetic field at a particular point inside the coil, which variables in our solution could be easily modified?