The magnetic field inside a long solenoid having 50 turns `cm^(-1)` is increased from `2.5 xx 10^(-3) T` to `2.5 T` when an iron core of cross-sectional area `4 cm^2` is inserted into it. Find (a) the current in the solenoid, (b) the magnetization `I` of the core and (c) the pole strength developed in the core.

Explanation

To solve the problem step by step, we will use the following information provided in the question:

1. The number of turns per unit length of the solenoid, \( n = 50 \, \text{turns/cm} = 5000 \, \text{turns/m} \).
2. The initial magnetic field \( B_1 = 2.5 \times 10^{-3} \, \text{T} \).
3. The final magnetic field \( B_2 = 2.5 \, \text{T} \).
4. The cross-sectional area of the iron core \( A = 4 \, \text{cm}^2 = 4 \times 10^{-4} \, \text{m}^2 \).
5. The permeability of free space \( \mu_0 = 4\pi \times 10^{-7} \, \text{T m/A} \).

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