Upon the insertion of an iron core with a cross-sectional area of 4 cm ^2 , the magnetic field inside a long solenoid having 50 turns cm ⁻¹ increases from 2.5 10⁻³ T to 2.5 T . Determine the magnetization I of the core.

Step-by-step solution

The initial magnetic field inside the solenoid without the core is given by: B₀ = ₀ H = 2.5 10⁻³ T The magnetic field after the insertion of the iron core is: B = ₀ (H + I) = 2.5 T From the above equations, we can write: B = B₀ + ₀ I Rearranging for the magnetization I : I = B - B₀ ₀ Substituting the given values: I = 2.5 - 2.5 10⁻³ 4 10⁻⁷ Since 2.5 10⁻³ is very small compared to 2.5 , we can approximate B - B₀ 2.5 T : I 2.5 4 3.14 10⁻⁷ I 2.5 12.56 10⁻⁷ I 1.99 10^6 A m ⁻¹ Rounding to the nearest given option, we ge