Q 12-05-020NEETJEE MainMedium
A solenoid of $1000$ turns per metre carries $2$ A. An iron core of relative permeability $400$ is inserted. The magnetic field inside is ($\mu_0 = 4\pi \times 10^{-7}$ T m/A)
Answer: (C) $0.32\pi$ T
Concept. The solenoid sets the magnetic intensity $H = nI$; the core multiplies the field: $B = \mu_0\mu_r H$.
Step 1. Magnetic intensity. $H = 1000 \times 2 = 2000$ A/m.
Step 2. Field with the core.
$$B = 4\pi \times 10^{-7} \times 400 \times 2000 = 0.32\pi\ \text{T} \approx 1.0\ \text{T}$$
Answer. $0.32\pi$ T (Option C).
Solution by Sreeraj P, M.Sc Physics