# 5.24. 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 B in the core for a magnetising current of 1.2 A?

Given,

Radius of ring, r = 15cm = 0.15m

Number of turns in the ring, n = 3500

Relative permeability of the ferromagnetic core, $\dpi{100} \mu_{r}$ = 800

Current in the Rowland ring, I = 1.2A

We know,

Magnetic Field due to a circular coil, B  = $\dpi{100} \frac{\mu_{r} \mu_{0}nI}{2\pi r}$

∴ B = $\dpi{100} \frac{4\pi\times10^{-7}\times800\times3500\times1.2}{2\pi \times0.15}$ = 4.48T

Therefore, the magnetic field B in the core for a magnetising current is 4.48 T

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