The magnetic field along the axis of an air-cored solenoid is 0.03 T. On placing an iron core inside the solenoid, the magnetic field becomes 1.5 T. The relative permeability of the iron core is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 50
Inside a long solenoid the magnetic intensity \( H=nI \) depends only on the turns and the current. So it is the same with and without the core. With air inside, the field is \( B_0=\mu_0H \). With the iron core, it becomes \( B=\mu_r\mu_0H \). So the relative permeability is the ratio of the two fields.
\( \begin{aligned} \mu_r &= \frac{B}{B_0} \\ &= \frac{1.5\,\mathrm{T}}{0.03\,\mathrm{T}} \\ &= 50 \end{aligned} \)