A Rowland ring of mean radius 15 cm has 3500 turns of wire wound on a ferromagnetic core of relative permeability 800.
Question:

A Rowland ring of mean radius 15 cm has 3500 turns of wire wound on a ferromagnetic core of relative permeability 800. What is the magnetic field in the core for a magnetising current of 1.2 A?

Solution:

Mean radius of a Rowland ring, r = 15 cm = 0.15 m

Number of turns on a ferromagnetic core, N = 3500

Relative permeability of the core material, $\mu_{r}=800$

Magnetising current, I = 1.2 A

The magnetic field is given by the relation:

$B=\frac{\mu_{r} \mu_{0} I N}{2 \pi r}$

Where,

μ0 = Permeability of free space = 4π × 10−7 Tm A−1

$B=\frac{800 \times 4 \pi \times 10^{-7} \times 1.2 \times 3500}{2 \pi \times 0.15}=4.48 \mathrm{~T}$

Therefore, the magnetic field in the core is 4.48 T.