A thin wire carrying a steady current \(I\) is bent into the shape of a regular planar polygon with \(n\) sides inscribed in a circle of radius \(R\). The magnitude of the magnetic field at the center of the polygon is given by the expression

\[ B(n) = \dfrac{\mu_0 n I}{2\pi R} \tan\left(\dfrac{\pi}{n}\right) \]

Which of the following statements correctly describes the behavior of \(B(n)\) in the limit as \(n \to \infty\), and provides the correct physical justification?