Ncert Exercises & Solutions

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 magnetizing current of 1.2 A?

Mean radius of Rowland ring, r= 15 cm =0.15 m
Number of turns on a feromagnetic core, N= 3500
Relative perme ability of the core material,

$μ_{r} = 800$
Magnetising curent, I=1.2 A
The magnetic field is given by the relation:

$B = \frac{μ_{r} μ_{0} I N}{2 π r}$

$W h e r e, μ_{0} = P e r m e a b i l i t y o f f r e e s p a c e = 4 π \times 10^{- 7} T m A^{- 1}$

$B = \frac{800 \times 4 π \times 10^{- 7} \times 1.2 \times 3500}{2 π \times 0.15} = 4.48 T$
Therefore, the magnetic field in the core is 4.48 T.

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