Final answer:
The magnetic field on the axis of a long solenoid with n turns per unit length carrying a current I is given by the formula B = μ₀nI, where μ₀ is the permeability of free space.
Step-by-step explanation:
The magnetic field on the axis of a long solenoid having n turns per unit length and carrying a current I is given by the formula B = μ₀nI. This equation represents the magnetic field strength inside a solenoid which is uniform both in magnitude and direction, assuming the solenoid is infinitely long or we are considering a point near the middle of the solenoid. Here, μ₀ is the permeability of free space and has the value of 4π x 10^-7 N/A^2. The field outside the solenoid is nearly zero due to the cylindrical symmetry of the arrangement.
For example, consider a solenoid that has a specified number of turns per meter and carries a current that is changing over time. If we have the rate at which the current changes, dI/dt, and other dimensions of the solenoid, we can compute the induced electromotive force (emf) in a coil placed inside the solenoid using Faraday's Law of electromagnetic induction.