Physics
Physics
Problem
A long air-cored solenoid of length and radius has turns uniformly distributed along its length. a. (i) Calculate the current required to establish a magnetic field of at an interior point on its axis. b. (ii) The solenoid is now completely filled with an iron core of relative permeability . Determine the new current that must be passed through the winding to maintain the same axial magnetic field of .Intuitive explanation
The key to solenoid problems is recognizing that a uniform coil creates a nearly uniform magnetic field inside—and the field strength depends only on how tightly the turns are packed (turns per unit length) and the current flowing through them. Rather than summing contributions from each loop, you can use the formula , where is the turn density. This transforms a potentially tedious calculation into a straightforward plug-in.
Intuitive explanation
The key to solenoid problems is recognizing that a uniform coil creates a nearly uniform magnetic field inside—and the field strength depends only on how tightly the turns are packed (turns per unit length) and the current flowing through them. Rather than summing contributions from each loop, you can use the formula , where is the turn density. This transforms a potentially tedious calculation into a straightforward plug-in.