The inductance of a solenoid with a cylindrical rod inserted inside can be calculated using the formula that incorporates the solenoid's physical parameters: radius R, length L, number of turns N, current I, and the rod's permeability μ. The presence of the rod alters the magnetic field and thus affects the overall inductance. Users are encouraged to share their attempts and specific challenges to receive targeted assistance. Understanding the relationship between these variables is crucial for solving the problem effectively. Engaging with the community can provide valuable insights and solutions.