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 pole strength developed in the core.

Step-by-step solution

Given: Initial magnetic field, B₀ = 2.5 10⁻³ T Final magnetic field, B = 2.5 T Cross-sectional area, A = 4 cm ^2 = 4 10⁻⁴ m ^2 The magnetic field inside the solenoid without the core is B₀ = ₀ H . With the iron core inserted, the magnetic field becomes B = ₀ (H + I) , where I is the intensity of magnetization of the core. Therefore, B = B₀ + ₀ I I = B - B₀ ₀ Since B₀ B , we can approximate B - B₀ B = 2.5 T . The pole strength m developed in the core is given by: m = I A B ₀ A Substituting the given values: m = 2.5