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 ?

Explanation

A Rowland ring is a toroid. The magnetic field in the ferromagnetic core of permeability `mu` , radius r, number of turns n and carrying current I is given by:
`B = mu xx n xx i`
`B = mu xx (N)/(2pi r) xx i`
` =mu_0 mu_r xx (Ni)/(2pi r) ` (where `mu_r` is the relative permeability of the core)
Here `mu_r = 800 , i = 1.2 A ,` number of turns, N = 3,500, radius of core, r= 15 cm = 0.15 m
Number of turns per unit length, `n =(N)/(2pi r) = (3,500)/(2pi xx 0.15) `
` rArr B = (4pi xx 10^(-7) xx 800 xx 3500 xx 1.2)/(2pi xx 0.15) = 4.48 T`