The magnetic field (B) inside a long solenoid having ' n ' turns per unit length and carrying current ' $i$…
- $\mu_0 \mathrm{ni}(1+\chi)$
- $\mu_0 \mathrm{ni}^2(1+\chi)$
- $\mu_0 \mathrm{ni} \chi$
- $\mu_0 \operatorname{ni}(1-\chi)$
Solution
Magnetic field enhancement in a solenoid with an iron core
The magnetic field inside a long solenoid with n turns per unit length carrying current i is given by $B_0 = \mu_0 n i$.
Introducing an iron core changes the permeability from $\mu_0$ to $\mu$, so the field becomes $B = \mu n i$.
The permeability of a magnetic material is defined by $\mu = \mu_0 (1 + \chi)$, where $\chi$ is the magnetic susceptibility.
Substituting this into the equation for the magnetic field yields $B = \mu_0 (1 + \chi) n i$.
Asked in: MHT CET 2025 (05 May Shift 2)