Final answer:
An electromagnet is a solenoid with a ferromagnetic core. The iron core enhances the magnetic field strength. To find the permeability of the iron, we can use the formula B = µ₀nI.
Step-by-step explanation:
An electromagnet is a solenoid with a ferromagnetic core. A solenoid is a long coil of wire that generates a magnetic field when an electric current is passed through it. When the solenoid is wrapped around an iron core, it becomes an electromagnet. The iron core enhances the magnetic field strength and makes it stronger.
In this case, the solenoid has an iron core, a length of 25 cm, and 100 turns of wire. When the current through the solenoid is 10 A, the magnetic field inside it is 2.0 T. To find the permeability of the iron, we can use the formula B = µ₀nI, where B is the magnetic field, µ₀ is the permeability of free space (4π x 10^-7 Tm/A), n is the number of loops per unit length, and I is the current. Rearranging the formula to solve for µ₀, we have µ₀ = B / (nI). Substituting the given values, µ₀ = 2.0 T / (100 / 0.25 m x 10 A) = 2.0 T / (400 A/m) = 5 x 10^-3 Tm/A.